Discrete Dynamics of Extremely Multistable Piecewise Chaotic System

In this paper we consider the discretization effects appearing in discrete models of the extremely multistable system while simulated by various numerical methods. In our study, we investigate the following set of methods: explicit, implicit, and semi-implicit Euler methods, composition diagonally implicit (CD) methods, explicit and implicit midpoint integrators. We use bifurcation diagrams for highlighting the features of dynamics under investigation introduced by various numerical methods. Significant discrepancies between the nonlinear behavior of discrete models obtained by different integration operators are observed and explained.