Chaos control of new Mathieu–Van der Pol systems with new Mathieu–Duffing systems as functional system by GYC partial region stability theory

In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve chaos control. Using the GYC partial region stability theory, the new Lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error. Numerical simulations are given for new Mathieu–Van der Pol system and new Mathieu–Duffing system to show the effectiveness of this strategy.