Fixed-time Adaptive Control for A New Three-dimensional Nonlinear System with Circular Equilibrium

Abstract

In this paper, we proposed a new nonlinear chaotic oscillator. The model of the system is given through a predefined form. Its unique property lies in the circle-shaped equilibrium. Both analysis and simulations are presented. In particular, the stability of the neighbourhood of the equilibrium point is analysed in terms of theoretical derivation and dynamic behaviour. Moreover than that, a robust control method of a category of three-dimensional chaotic systems is designed. And the final simulation results proved the effectiveness of the controllers.