Analysis, Stabilization, and DSP-Based Implementation of a Chaotic System with Nonhyperbolic Equilibrium

Abstract

This paper reports an autonomous dynamical system, and it finds that one nonhyperbolic zero equilibrium and two hyperbolic nonzero equilibria coexist in this system. Thus, it is difficult to demonstrate the existence of chaos by Šil’nikov theorem. Consequently, the topological horseshoe theory is adopted to rigorously prove the chaotic behaviors of the system in the phase space of Poincaré map. Then, a single control scheme is designed to stabilize the dynamical system to its zero-equilibrium point. Besides, to verify the theoretical analyses physically, the attractor and stabilization scheme are further realized via DSP-based technique.