Dynamics of Chaotic 3D Attractors: Part 1

Gallery of more than 100 three-dimensional attractors plotted by me in MATLAB based on General Algorithm of The Explicit Runge—Kutta Method.

A fair number of attractors I found on Jürgen Mayer's personal website, you can find references to primary sources there, so if some attractors lack references, those attractors were found there. For attractors that have been found already by me, I will leave a reference to the primary source.

The plots are also available on Pinterest and Behance:

P.S. I give the title of attractors as the surnames of the authors of the paper where the attractor was found. For papers with a large number of authors, I take only the first 3 surnames.

Relevant Repositories:

• Dynamics of Chaotic 3D Attractors: Part 2
• Dynamics Of Hyperchaotic High-Dimensional Attractors

The Lorenz Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \sigma(y - x), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x(\rho - z) - y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = xy - \beta z, \end{cases} $$

$$ \begin{bmatrix} \sigma\\ \rho\\ \beta \end{bmatrix} = \begin{bmatrix} 10 \\ 28 \\ \dfrac{8}{3} \end{bmatrix}. $$

The Lorenz Mod 1 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-\alpha x+y^2-z^2+\alpha\varsigma, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x\left(y-\beta z\right)+\delta, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-z+x\left(\beta y+z\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 0.1\\ 4\\ 14\\ 0.08 \end{bmatrix}. $$

The Lorenz Mod 2 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-\alpha x+y^2-z^2+\alpha\varsigma, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x\left(y-\beta z\right)+\delta, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-z+x\left(\beta y+z\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 0.9\\ 5\\ 9.9\\ 1 \end{bmatrix}. $$

The Lotka—Volterra Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=x-xy+\varsigma x^2-\alpha z x^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-y+xy, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\beta z +\alpha z x^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 2.9851\\ 3\\ 2 \end{bmatrix}. $$

The Aizawa Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = (z - \beta)x - \delta y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \delta x + (z - \beta)y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \varsigma + \alpha z - \dfrac{z^3}{3} - \left(x^2 + y^2\right)\left(1 + \varepsilon z\right) + \xi zx^3, \end{cases} $$

$$ \begin{bmatrix} \alpha \\ \beta \\ \varsigma \\ \delta \\ \varepsilon \\ \xi \end{bmatrix}= \begin{bmatrix} 0.95 \\ 0.7 \\ 0.6 \\ 3.5 \\ 0.25 \\ 0.1 \end{bmatrix}. $$

The Tamari Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =\left(x-\alpha y\right)\cos z-\beta y \sin z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \left(x+\gamma y\right)\sin z +\delta y\cos z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \varepsilon +\kappa z+\xi\arctan\left(\dfrac{1-\varsigma}{1-\omega}xy\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \gamma\\ \delta\\ \varepsilon\\ \kappa\\ \xi\\ \varsigma\\ \omega \end{bmatrix}= \begin{bmatrix} 1.013\\ -0.011\\ 0.02\\ 0.96\\ 0\\ 0.01\\ 1\\ 0.05\\ 0.05 \end{bmatrix}. $$

The Halvorsen Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -\alpha x-4y-4z-y^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =-\alpha y-4z-4x-z^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\alpha z-4x-4y-x^2, \end{cases} $$

$$ \alpha=1.4. $$

The Thomas Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =-\beta x+\sin y,\\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\beta y + \sin z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\beta z + \sin x, \end{cases} $$

$$ \beta=0.19. $$

The ACT Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(x-y\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -4\alpha y +xz+\varsigma x^3, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\delta\alpha z +xy+\beta z^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \delta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 1.8\\ -0.07\\ 1.5\\ 0.02 \end{bmatrix}. $$

The Hindmarsh—Rose Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -\alpha x^3 +\beta x^2+y -z+\iota, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =-\delta x^2-y+\varsigma, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \rho\left(\xi\left(x-\chi\right)-z\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \iota\\ \rho\\ \xi\\ \chi \end{bmatrix}= \begin{bmatrix} 1\\ 3\\ 1\\ 5\\ 3.25\\ 0.006\\ 4\\ -1.6 \end{bmatrix}. $$

The Rucklidge Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =-\kappa x+\alpha y -yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -z+y^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \kappa \end{bmatrix}= \begin{bmatrix} 6.7\\ 2 \end{bmatrix}. $$

The Arneodo Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\alpha x -\beta y -z+\varsigma x^3, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} -5.5\\ 3.5\\ -1 \end{bmatrix}. $$

The 3-Cells CNN Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -x+\alpha f(x)-\delta f(y)- \delta f(z), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -y-\delta f(x)+\beta f(y)-\varsigma f(z), \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -z -\delta f(x)+\varsigma f(y) + f(z), \end{cases} $$

$$ f\left(\omega\right)=\dfrac{1}{2}\left(\left|\omega+1\right|-\left|\omega-1\right|\right), $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 1.24\\ 1.1\\ 4.4\\ 3.21 \end{bmatrix}. $$

The Dadras Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =y-\rho x+\sigma yz,\\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \xi y-xz+z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \varsigma xy-\varepsilon z, \end{cases} $$

$$ \begin{bmatrix} \rho\\ \sigma\\ \xi\\ \varsigma\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 3\\ 2.7\\ 1.7\\ 2\\ 9 \end{bmatrix}. $$

The Rössler Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =-y-z,\\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x+\alpha y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \beta+z\left(x-\varsigma\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}=\begin{bmatrix} 0.1\\ 0.1\\ 14 \end{bmatrix}. $$

The Finance Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \left(\dfrac{1}{\beta}-\alpha\right)x+z+xy, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\beta y-x^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -x -\varsigma z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}=\begin{bmatrix} 0.001\\ 0.2\\ 1.1 \end{bmatrix}. $$

The Chen—Celikovsky Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha\left(y-x\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-xz+\varsigma y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= xy-\beta z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}=\begin{bmatrix} 36\\ 3\\ 20 \end{bmatrix}. $$

The Hadley Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -y^2-z^2-\alpha x+\alpha\varsigma, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =xy -\beta xz-y+\delta, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} =\beta xy+xz-z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 0.2\\ 4\\ 8\\ 1 \end{bmatrix}. $$

The Wang Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(x-y\right)-yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\beta y+xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} =-\varsigma z+\delta x+xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 0.977\\ 10\\ 4\\ 0.1 \end{bmatrix}. $$

The Wimol—Banlue Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =y-x, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -z\tanh x, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\alpha+xy+|y|, \end{cases} $$

$$ \alpha = 2. $$

The Deng Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = z (\lambda x - \mu y )+ (2-z) \left[ \alpha x \left( 1-\dfrac{x^2+y^2}{\rho^2} \right) -\beta y \right], \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = z ( \mu x +\lambda y) + (2-z) \left[ \alpha y \left( 1- \dfrac{x^2+y^2}{\rho^2} \right)+\beta x \right], \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \dfrac{1}{\varepsilon} \left[z ( (2-z) \left( \varphi (z-2)^2+\psi \right) - \delta x)\left(z+\xi \left( x^2+y^2 \right)-\eta \right)-\varepsilon \varsigma(z-1) \right], \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \xi \\ \eta\\ \rho \\ \varepsilon\\ \lambda\\ \mu\\ \varphi\\ \psi \end{bmatrix}= \begin{bmatrix} 2.8\\ 5\\ 1\\ 0.1\\ 0.05\\ 3.312\\ 10\\ 0.1\\ -2\\ 1.155\\ 3\\ 0.8 \end{bmatrix}. $$

The Shimizu—Morioka Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=\left(1-z\right)x-\alpha y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x^2-\beta z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.75\\ 0.45 \end{bmatrix}. $$

The Nose—Hoover Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x+yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\alpha-y^2, \end{cases} $$

$$ \alpha=1.5. $$

The Wang—Sun Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =\alpha x +\varsigma yz,\\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \beta x +\delta y -xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \varepsilon z +\xi xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \delta\\ \varepsilon\\ \xi\\ \varsigma \end{bmatrix}=\begin{bmatrix} 0.2\\ -0.01\\ -0.4\\ -1\\ -1\\ 1 \end{bmatrix}. $$

The Xing—Yun Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha\left(y-x\right)+yz^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=\beta\left(x+y\right)-xz^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\varsigma z+\varepsilon y +xyz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 50\\ 10\\ 13\\ 6 \end{bmatrix}. $$

The Lü—Chen Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=- \dfrac{\alpha\beta}{\alpha+\beta}x -yz+\varsigma, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=\alpha y +xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\beta z+xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} -10\\ -4\\ 18.1 \end{bmatrix}. $$

The Burke—Shaw Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-\alpha\left(x+y\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-y-\alpha xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\alpha xy +\beta, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 10\\ 4.272 \end{bmatrix}. $$

The Zhou—Chen Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x+\beta y +yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =\varsigma y-xz+\delta yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} =\varepsilon z-xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 2.97\\ 0.15\\ -3\\ 1\\ -8.78 \end{bmatrix}. $$

The Genesio—Tesi Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\varsigma x-\beta y-\alpha z+x^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 0.44\\ 1.1\\ 1 \end{bmatrix}. $$

The Yu—Wang Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =\beta x-\varsigma xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \exp{(xy)}-\delta z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 10\\ 40\\ 2\\ 2.5 \end{bmatrix}. $$

The Sakarya Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -x+y+yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =-x-y+\alpha xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = z-\beta xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.4\\ 0.3 \end{bmatrix}. $$

The Chua Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha\left(y-x-\left(\varsigma x + \dfrac{1}{2}\left(\delta-\varsigma\right)\left(\left|x+1\right|-\left|x-1\right|\right)\right)\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x-y+z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\beta y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} \dfrac{78}{5}\\ \dfrac{1279}{50}\\ -\dfrac{5}{7}\\ -\dfrac{8}{7} \end{bmatrix}. $$

The Chua Cubic Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x^3-\varsigma x\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x-y+z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\beta y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 10\\ 16\\ -0.143 \end{bmatrix}. $$

The Modified Chua Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =\alpha\left(y+\delta\sin{\left(\dfrac{\pi x}{2\varsigma}+\varepsilon\right)}\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x-y+z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = -\beta y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 10.82\\ 14.286\\ 1.3\\ 0.11\\ 0 \end{bmatrix}. $$

The Muthuswamy—Chua Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-\dfrac{x}{3}+\dfrac{y}{2}-\dfrac{yz^2}{2}, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=y-\alpha z-yz, \end{cases} $$

$$ \alpha=0.6. $$

The Moore—Spiegel Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-z-\left(\beta-\alpha+\alpha x^2\right)y-\beta x, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 100\\ 26 \end{bmatrix}. $$

The Coullet Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\alpha x + \beta y + \varsigma z + \delta x^3, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 0.8\\ -1.1\\ -0.45\\ -1 \end{bmatrix}. $$

The Sprott A Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x+yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-y^2 \end{cases} $$

The Sprott B Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-xy \end{cases} $$

The Sprott C Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-x^2 \end{cases} $$

The Sprott D Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x+z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=xz + \alpha y^2, \end{cases} $$

$$ \alpha=3. $$

The Sprott E Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x^2-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-\alpha x, \end{cases} $$

$$ \alpha=4. $$

The Sprott F Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y+z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x+\alpha y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x^2-z, \end{cases} $$

$$ \alpha=\dfrac{1}{2}. $$

The Sprott G Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha x + z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=xz-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-x+y, \end{cases} $$

$$ \alpha=\dfrac{2}{5}. $$

The Sprott H Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-y+z^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x+\alpha y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x-z, \end{cases} $$

$$ \alpha=\dfrac{1}{2}. $$

The Sprott I Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x+z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x+y^2-z, \end{cases} $$

$$ \alpha=-\dfrac{1}{5}. $$

The Sprott J Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-\alpha y +z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= -x+y+y^2, \end{cases} $$

$$ \alpha=2. $$

The Sprott K Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=xy-z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x+\alpha z, \end{cases} $$

$$ \alpha=\dfrac{3}{10}. $$

The Sprott L Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y+\alpha z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=\beta x^2 - y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-x, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 3.9 \\ 0.9 \end{bmatrix}. $$

The Sprott M Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x^2-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\alpha + \alpha x+y, \end{cases} $$

$$ \alpha=\dfrac{17}{10}. $$

The Sprott N Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-\alpha y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x+z^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1+y-\alpha z, \end{cases} $$

$$ \alpha=2. $$

The Sprott O Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x-z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x+xz+\alpha y, \end{cases} $$

$$ \alpha=\dfrac{27}{10}. $$

The Sprott P Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha y + z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x+y^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x+y, \end{cases} $$

$$ \alpha=\dfrac{27}{10}. $$

The Sprott Q Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x - y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\alpha x +y^2+\beta z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 3.4 \\ 0.5 \end{bmatrix}. $$

The Sprott R Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha -y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=\beta +z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=xy-z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.9 \\ 0.4 \end{bmatrix}. $$

The Sprott S Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-x+\alpha y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=x +z^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1+x, \end{cases} $$

$$ \alpha=4. $$

The TSUCS1 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x\right)+\varsigma xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \varepsilon y-xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \beta z+xy-\delta x^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix} = \begin{bmatrix} 40\\ 0.833\\ 0.5\\ 0.65\\ 20 \end{bmatrix}. $$

The TSUCS2 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x\right)+\delta xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \varsigma x-xz+\xi y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \beta z+xy-\varepsilon x^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon\\ \xi \end{bmatrix} = \begin{bmatrix} 40\\ 1.833\\ 55\\ 0.16\\ 20\\ 0.65 \end{bmatrix}. $$

The Rikitake Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-\beta x + zy, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-\beta y + \left(z-\alpha\right)x, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 5 \\ 2 \end{bmatrix}. $$

The Newton—Leipnik Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=-\alpha x+y+10yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x-0.4y+5xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\beta z-5xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.4 \\ 0.175 \end{bmatrix}. $$

The Four—Wing 1 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x -\beta yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\varsigma y +xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \varepsilon x -\delta z +xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 4\\ 6\\ 10\\ 5\\ 1 \end{bmatrix}. $$

The Four—Wing 2 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x+\beta y+\varsigma yz \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \delta y - xz \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \varepsilon z +\xi x y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon\\ \xi \end{bmatrix}= \begin{bmatrix} -14\\ 5\\ 1\\ 16\\ -43\\ 1 \end{bmatrix}. $$

The Four—Wing 3 Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=x+y+yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=yz-xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=1-\alpha xy -z \end{cases} $$

$$ \alpha = 1. $$

The Zhou Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha\left(y-x\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=\beta x - xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=xy+\varsigma z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 10 \\ 16\\ -1 \end{bmatrix}. $$

The Elhadj—Sprott Attractor

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=\alpha\left(y-x\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-\alpha x -\beta yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\varsigma+y^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 40 \\ 33\\ 10 \end{bmatrix}. $$

The Sprott—Jafari Attractor

Reference:
Jafari, S., Sprott, J. C., & Nazarimehr, F. (2015). Recent new examples of hidden attractors. The European Physical Journal Special Topics, 224(8), 1469–1476.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -x+yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= z+\alpha x^2-y^2-\beta, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 8.888\\ 4 \end{bmatrix}. $$

The Sprott Strange Multifractal Attractor

Reference:
Sprott, J. (2020). Do We Need More Chaos Examples?. Chaos Theory and Applications, 2(2), 49-51.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t}=y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t}=-x-\text{sgn}(z) y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=y^2-\exp\left(-x^2\right) \end{cases} $$

The Liu Attractor

Reference:
Liu, C. (2009). A novel chaotic attractor. Chaos, Solitons & Fractals, 39(3), 1037–1045.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x+yz\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \beta y - \varepsilon xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \varsigma y-\delta z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 1\\ 2.5\\ 1\\ 4\\ 1 \end{bmatrix}. $$

The Sundarapandian—Pehlivan Attractor

Reference:
Sundarapandian, V., & Pehlivan, I. (2012). Analysis, control, synchronization, and circuit design of a novel chaotic system. Mathematical and Computer Modelling, 55(7-8), 1904–1915.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha y -x, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\beta x - z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \varsigma z + xy^2-x, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 1\\ 0.46\\ 0.46 \end{bmatrix}. $$

The Sundarapandian Attractor

Reference:
Sundarapandian, V. (2013). Analysis and anti - synchronization of a novel chaotic system via active and adaptive controllers. Journal of Engineering Science and Technology Review, 6(4), 45–52.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y -x\right)+yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \beta x +\varsigma y -xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= -\delta z +x^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 21.5\\ 20.6\\ 11\\ 6.4 \end{bmatrix}. $$

The Pehlivan Attractor

Reference:
Pehlivan, I. (2011). Four-scroll stellate new chaotic system. Optoelectronics and Advanced Materials - Rapid Communications - OAM-RC - INOE 2000.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -\alpha x + y + yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x-\alpha y +\beta xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \varsigma z - \beta x y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 4\\ 0.5\\ 0.6 \end{bmatrix}. $$

The Vaidyanathan Hyperbolic Sinusoidal Attractor

Reference:
Vaidyanathan, S. (2013). Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters. Journal of Engineering Science and Technology Review, 6(4), 53–65.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x\right)+yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \beta x - \varsigma xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\delta z + \sinh\left(xy\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 10\\ 92\\ 2\\ 10 \end{bmatrix}. $$

The Vaidyanathan Hyperbolic Cosinusoidal Attractor

Reference:
Vaidyanathan, S. (2013). Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters. Journal of Engineering Science and Technology Review, 6(4), 53–65.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x\right)+yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \beta x - \varsigma xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\delta z + \cosh\left(xy\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta \end{bmatrix}= \begin{bmatrix} 10\\ 98\\ 2\\ 10 \end{bmatrix}. $$

The Neamah—Shukur Attractor

Reference:
Neamah, A. A., & Shukur, A. A. (2023). A novel conservative chaotic system involved in hyperbolic functions and its application to design an efficient colour image encryption scheme. Symmetry, 15(8), 1511.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} =-x-yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \cosh y-1-\alpha\cos x^2-\beta\cos y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 1\\ 0.3 \end{bmatrix}. $$

The Li—Ou Attractor

Reference:
Li, X., & Ou, Q. (2010). Dynamical properties and simulation of a new Lorenz-like chaotic system. Nonlinear Dynamics, 65(3), 255–270.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha\left(y-x\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \varsigma y-xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=-\beta z + \delta x^2 +\varepsilon xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix}= \begin{bmatrix} 10\\ 3\\ 6\\ 1\\ 0 \end{bmatrix}. $$

The Sprott—Li Chaotic Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = 1+yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= y^2+\alpha yz, \end{cases} $$

$$ \alpha=2. $$

The Sprott—Li SL$_1$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -x+\alpha y^2 - xy, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= z^2 -\beta xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 2\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_2$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -\alpha x + xy, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = z^2 + xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= y^2 -\beta yz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 2\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_3$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = x + \alpha y^2-z^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x^2-\beta y^2, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= xz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 2.4\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_4$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -x + \beta y^2 + xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= -\alpha xy + yz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.1\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_5$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -x+\alpha z^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = z^2 - \beta xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= xy - yz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 1\\ 2 \end{bmatrix}. $$

The Sprott—Li SL$_6$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y - z^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\alpha xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= x^2 - yz, \end{cases} $$

$$ \alpha=0.9. $$

The Sprott—Li SL$_7$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -y-yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x^2+\alpha xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= z^2 + \beta yz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 14\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_8$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y - y^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \alpha z^2 + xy, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= -x^2 - \beta xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.3\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_9$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = \alpha y^2 - xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= x^2 +xy-\beta xz, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.4\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_{10}$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y + \alpha xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = xy - xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= x^2 +\beta xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.2\\ 3 \end{bmatrix}. $$

The Sprott—Li SL$_{11}$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y + y^2 - \alpha yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -z^2+\beta yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.9\\ 1 \end{bmatrix}. $$

The Sprott—Li SL$_{12}$ Attractor

Reference:
Li, C., & Sprott, J. C. (2014). Chaotic flows with a single nonquadratic term. Physics Letters A, 378(3), 178–183.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -y+x^2-y^2, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \alpha x + \beta xy, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 0.3\\ 1 \end{bmatrix}. $$

The Zhang—Liao Attractor

Reference:
Zhang, J., & Liao, X. (2017). Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse. AEU - International Journal of Electronics and Communications, 75, 82–90.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y - x\left(\beta+0.5\left(\alpha-\beta\right)\left(\text{sgn}\left(z+1\right)-\text{sgn}\left(z-1\right)\right)\right)+\dfrac{\varepsilon}{\vartheta}\cos\left(\vartheta t\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\varsigma y-\varsigma x, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \delta x, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon\\ \vartheta \end{bmatrix}= \begin{bmatrix} -1.03\\ -0.5\\ 0.98\\ 1\\ 0.15\\ 0.75 \end{bmatrix}. $$

The Kountchou—Louodop Attractor

Reference:
Kountchou, M., Louodop, P., Bowong, S., Fotsin, H., & Kurths, J. (2016). Optimal Synchronization of a Memristive Chaotic Circuit. International Journal of Bifurcation and Chaos, 26(06), 1650093.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \cos\left(\beta t\right)+\alpha y\left(1+z^2-z^4\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x-y\cos\left(\beta t\right), \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= -\varsigma y, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix}= \begin{bmatrix} 2\\ 2.5\\ 6 \end{bmatrix}. $$

The Sambas—Vaidyanathan—Zhang Attractor

Reference:
Sambas, A., Vaidyanathan, S., Zhang, S., Zeng, Y., Mohamed, M. A., & Mamat, M. (2019). A New Double-Wing Chaotic System with Coexisting Attractors and Line Equilibrium: Bifurcation Analysis and Electronic Circuit Simulation. IEEE Access, 1–1.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} =yz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = x-y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \alpha\left|x\right|-\beta x^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 5\\ 2 \end{bmatrix}. $$

The Kingni—Jafari—Simo Attractor

Reference:
Kingni, S. T., Jafari, S., Simo, H., & Woafo, P. (2014). Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form. The European Physical Journal Plus, 129(5).

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = -z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -x-z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= 3x-\alpha y + x^2-z^2-yz+\beta, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix}= \begin{bmatrix} 1.3\\ 1.01 \end{bmatrix}. $$

The Nazarimehr—Sprott Attractor

Reference:
Nazarimehr, F., & Sprott, J. C. (2020). Investigating chaotic attractor of the simplest chaotic system with a line of equilibria. The European Physical Journal Special Topics, 229(6-7), 1289–1297.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha y, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = xz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= y-z-y^2, \end{cases} $$

$$ \alpha=289. $$

The Sun—Tian—Fu Attractor

Reference:
Sun, M., Tian, L., & Fu, Y. (2007). An energy resources demand–supply system and its dynamical analysis. Chaos, Solitons & Fractals, 32(1), 168–180.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x\left(1 - \dfrac{x}{\varphi}\right) - \beta\left(y + z\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\varsigma y - \delta z + \xi x\left[\vartheta - \left(x - z\right)\right], \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = \eta z\left(\zeta x - \varepsilon\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \xi \\ \eta\\ \zeta \\ \varepsilon\\ \varphi\\ \vartheta \end{bmatrix} = \begin{bmatrix} 0.09\\ 0.15\\ 0.06\\ 0.082\\ 0.07\\ 0.2\\ 0.5\\ 0.4\\ 1.8\\ 1 \end{bmatrix}. $$

The Wang—Sun—Cang Signum Attractor

Reference:
Wang, Z., Sun, Y., & Cang, S. (2011). Acta Physica Polonica B, 42(2), 235.
Herrera-Charles, R., Afolabi, O. M., Núñez-Pérez, J. C., & Ademola, V. A. (2024). Secure communication based on chaotic spherical 3D attractors. In Applications of Digital Image Processing XLVII (Vol. 13137, pp. 78-89).

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x - \beta y + \varsigma z + 2\text{sgn}\left(\sin y\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\delta xz+\xi+ \eta x, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \zeta xy + \varepsilon yz + \varphi z + \vartheta, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \xi \\ \eta\\ \zeta \\ \varepsilon\\ \varphi\\ \vartheta \end{bmatrix} = \begin{bmatrix} -4.1\\ 1.2\\ 13.45\\ 1.6\\ 0.161\\ 0\\ 2.76\\ 0.6\\ 13.13\\ 3.5031 \end{bmatrix}. $$

The Akgul—Hussain—Pehlivan Attractor

Reference:
Akgul, A., Hussain, S., & Pehlivan, I. (2016). A new three-dimensional chaotic system, its dynamical analysis and electronic circuit applications. Optik - International Journal for Light and Electron Optics, 127(18), 7062–7071.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha \left(x-y\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -4\alpha y + xz+\varsigma x^3, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\alpha\delta z + x^3y+\beta z^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \end{bmatrix}= \begin{bmatrix} 1.8\\ -0.07\\ 0.12\\ 1.5 \end{bmatrix}. $$

The Wang—Sun—Cang Hyperbolic Tangent Attractor

Reference:
Wang, Z., Sun, Y., & Cang, S. (2011). Acta Physica Polonica B, 42(2), 235.
Herrera-Charles, R., Afolabi, O. M., Núñez-Pérez, J. C., & Ademola, V. A. (2024). Secure communication based on chaotic spherical 3D attractors. In Applications of Digital Image Processing XLVII (Vol. 13137, pp. 78-89).

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x - \beta y + \varsigma z + 2\tanh\left(100\sin y\right), \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\delta xz+\xi+ \eta x, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}= \zeta xy + \varepsilon yz + \varphi z + \vartheta, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \xi \\ \eta\\ \zeta \\ \varepsilon\\ \varphi\\ \vartheta \end{bmatrix} = \begin{bmatrix} -4.1\\ 1.2\\ 13.45\\ 1.6\\ 0.161\\ 0\\ 2.76\\ 0.6\\ 13.13\\ 3.5031 \end{bmatrix}. $$

The Huang—Yang Attractor (Chemical Chaotic Reactor)

Reference:
Huang, Y., & Yang, X.-S. (2005). Chaoticity of some chemical attractors: a computer assisted proof. Journal of Mathematical Chemistry, 38(1), 107–117.
Vaidyanathan, S. (2015). A Novel Chemical Chaotic Reactor System and its Adaptive Control. International Journal of ChemTech Research, 8(11), 654–668.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha x-\delta x^2-xy-xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = xy-\varsigma y, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=\beta z-xz-\varepsilon z, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma\\ \delta\\ \varepsilon \end{bmatrix} = \begin{bmatrix} 30\\ 16.5\\ 10\\ 0.5\\ 0.5 \end{bmatrix}. $$

The Wang—Hu—Tian Attractor

Reference:
Wang, Q., Hu, C., Tian, Z., Wu, X., Sang, H., & Cui, Z. (2023). A 3D memristor-based chaotic system with transition behaviors of coexisting attractors between equilibrium points. Results in Physics, 56, 107201.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha y +\beta\left(0.1 + 0.5y^2\right)z, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = z, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=x-\varsigma y -z - 2.682\cdot10^{-4}\sinh\left(4.0485x\right), \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta\\ \varsigma \end{bmatrix} = \begin{bmatrix} 2\\ 2.5\\ 2 \end{bmatrix}. $$

The Qiu—Xu—Jiang Attractor

Reference:
Qiu, H., Xu, X., Jiang, Z., Sun, K., & Cao, C. (2023). Dynamical behaviors, circuit design, and synchronization of a novel symmetric chaotic system with coexisting attractors. Scientific Reports, 13(1).

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = y-2xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -x+0.5\left(1-x^2\right)y-0.5yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t}=0.1xy+\alpha x^2-0.8, \end{cases} $$

$$ \alpha = 0.21. $$

The Vaidyanathan—Volos Attractor

Reference:
Vaidyanathan, S., & Volos, C. (2015). Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Archives of Control Sciences, 25(3), 333–353.

$$ \begin{cases} \dfrac{\mathrm{d}x}{\mathrm{d}t} = \alpha y + xz, \\ \dfrac{\mathrm{d}y}{\mathrm{d}t} = -\beta x + yz, \\ \dfrac{\mathrm{d}z}{\mathrm{d}t} = 1 - x^2 - y^2, \end{cases} $$

$$ \begin{bmatrix} \alpha\\ \beta \end{bmatrix} = \begin{bmatrix} 0.05\\ 1 \end{bmatrix}. $$