Table 1 Existing 2D chaotic systems used in the comparison.

Hua et al.¹⁴

\({\left\{ \begin{array}{ll} x_{i+1} = \cos (4ax_i(1 - x_i)) + b\sin (\pi y_i + 1) \\ y_{i+1} = \sin (4ay_i(1 - y_i)) + b\sin (\pi x_i + 1) \end{array}\right. }\)

a, b

Gao ¹⁵

\({\left\{ \begin{array}{ll} x_{i+1} = \sin \left( h\frac{\pi }{\sin (y_i)}\right) \\ y_{i+1} = r\sin (\pi x_iy_i) \end{array}\right. }\)

h, r

Teng et al. ¹⁶

\({\left\{ \begin{array}{ll} x_{i+1} = \sin \left( \frac{\pi }{\alpha }\right) \sin \left( \frac{\alpha }{\sin (y_i)}\right) \\ y_{i+1} = \beta \sin (\pi (x_i + y_i)) \end{array}\right. }\)

\(\alpha , \beta\)

Sun¹⁷

\({\left\{ \begin{array}{ll} x_{i+1} = r\sin (\pi (y_i + h))\sin \left( \frac{ar}{x_i}\right) \\ y_{i+1} = r\sin (\pi (kx_{i+1} + h))\sin \left( \frac{ar}{x_i}\right) \end{array}\right. }\)

a, h, k, r

Zhu et al.¹⁸

\({\left\{ \begin{array}{ll} x_{i+1} = x_i + \frac{h'}{\Gamma (1 + \nu )}\cos \left( \frac{2\nu x_i}{\mu x_i^4 - 1}\right) \\ y_{i+1} = y_i + \frac{h'}{\Gamma (1 + \nu )}\cos (\mu r(x_i + y_i)) \end{array}\right. }\)

\(\mu , h', \nu , r\)

Nan et al.¹⁹

\({\left\{ \begin{array}{ll} x_{i+1} = \cos \left( \pi ^2(4\mu x_i(1 - x_i)) + p(1 - y_i^2)\right) + \frac{\pi }{2} \\ y_{i+1} = \cos \left( \pi ^2(4\mu y_i(1 - y_i)) + p(x_{i+1}(1 - x_i^2))\right) + \frac{\pi }{2} \end{array}\right. }\)

\(\mu , p\)