Two Simplest Quadratic Chaotic Maps Without Equilibrium
Shirin Panahi
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
Julien C. Sprott
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA
Sajad Jafari
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
Received February 2, 2018; Revised May 11, 2018
Two simple chaotic maps without equilibria are
proposed in this paper. All nonlinearities are quadratic and the
functions of the right-hand side of the equations are
continuous. The procedure of their design is explained and their
dynamical properties such as return map, bifurcation diagram,
Lyapunov exponents, and basin of attraction are investigated.
These maps belong to the hidden attractor category which is a
newly introduced category of dynamical system.