Dynamics of Nonlinear Attractors

This is where I'll post attractors I've plotted using explicit Runge-Kutta methods. The vast majority of attractors I've found on Jürgen Mayer's personal website, where you can find a list of sources where each attractor was found. To the attractors I found not using this site, I will add a source and the title of these attractors will be up to my imagination..

The plots are also available on Pinterest and Behance:

The Lorenz Attractor

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

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

The Lorenz Mod 1 Attractor

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

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

The Lorenz Mod 2 Attractor

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

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

The Lotka—Volterra Attractor

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

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

The Aizawa Attractor

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

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

The Tamari Attractor

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

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

The Halvorsen Attractor

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

$$ \alpha=1.4. $$

The Thomas Attractor

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

$$ \beta=0.19. $$

The ACT Attractor

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

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

The Hindmarsh—Rose Attractor

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

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

The Rucklidge Attractor

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

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

The Arneodo Attractor

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

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

The 3-Cells CNN Attractor

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

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

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

The Dadras Attractor

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

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

The Rössler Attractor

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

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

The Finance Attractor

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

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

The Chen—Celikovsky Attractor

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

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

The Hadley Attractor

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

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

The Wang Attractor

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

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

The Wimol—Banlue Attractor

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

$$ \alpha = 2. $$

The Deng Attractor

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

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

The Shimizu—Morioka Attractor

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

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

The Nose—Hoover Attractor

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

$$ \alpha=1.5. $$

The Wang—Sun Attractor

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

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

The Xing—Yun Attractor

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

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

The Lü—Chen Attractor

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

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

The Burke—Shaw Attractor

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

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

The Zhou—Chen Attractor

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

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

The Genesio—Tesi Attractor

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

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

The Yu—Wang Attractor

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

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

The Sakarya Attractor

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

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

The Chua Attractor

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

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

The Chua Cubic Attractor

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

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

The Modified Chua Attractor

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

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

The Muthuswamy—Chua Attractor

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

$$ \alpha=0.6. $$

The Moore—Spiegel Attractor

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

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

The Coullet Attractor

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

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

The Sprott A Attractor

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

The Sprott B Attractor

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

The Sprott C Attractor

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

The Sprott D Attractor

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

$$ \alpha=3. $$

The Sprott E Attractor

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

$$ \alpha=4. $$

The Sprott F Attractor

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

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

The Sprott G Attractor

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

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

The Sprott H Attractor

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

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

The Sprott I Attractor

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

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

The Sprott J Attractor

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

$$ \alpha=2. $$

The Sprott K Attractor

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

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

The Sprott L Attractor

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

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

The Sprott M Attractor

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

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

The Sprott N Attractor

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

$$ \alpha=2. $$

The Sprott O Attractor

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

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

The Sprott P Attractor

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

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

The Sprott Q Attractor

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

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

The Sprott R Attractor

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

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

The Sprott S Attractor

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

$$ \alpha=4. $$

The TSUCS1 Attractor

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

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

The TSUCS2 Attractor

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

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

The Rikitake Attractor

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

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

The Newton—Leipnik Attractor

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

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

The Four—Wing 1 Attractor

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

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

The Four—Wing 2 Attractor

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

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

The Four—Wing 3 Attractor

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

$$ \alpha = 1. $$

The Zhou Attractor

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

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

The Elhadj—Sprott Attractor

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

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

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.

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

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

The Sprott Strange Multifractal Attractor

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

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

The Liu Attractor

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

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

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

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.

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

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

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.

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

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

The Pehlivan Attractor

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

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

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

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.

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

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

The Vaidyanathan Hyperbolic Cosinusoidal Attractor