On the dynamics and chaos control of two discrete systems related to a singularly perturbed equation

Abstract

This research paper focuses on investigating the dynamics and chaos control of two discrete systems corresponding to the singularly perturbed equation associated to the Hénon difference equation with continuous arguments. We investigate the local stability of the two systems. To achieve chaos control, we employ the state feedback control method for both systems. Numerical simulations are conducted to gain insights into the qualitative behavior of these systems. By conducting numerical simulations, we gain valuable insights into the role played by the perturbation parameter and the discrete delays in the bifurcation behavior of each system. Furthermore, we demonstrate the practical application of the chaos control method through the implementation of an on-off strategy.

Keywords

• Chaos control
• Singular perturbation
• Stability
• Bifurcation
• Hénon map