Existence of attractor and control of a 3D differential system

Abstract

This paper analyzes the orbit of a three-dimensional differential system based on the Shilnikov criterion. It also applies the Shilnikov method of constructing a heteroclinic connection between saddle focus equilibrium points of the system, proving that the system possesses “horseshoe” chaos. In addition, adaptive backstepping design is used to control this system with three unknown key parameters, and an algorithm of this controller is presented. Finally, we give some numerical simulation studies of the system in order to verify the analytic results.