Suppressing Chaos for a Fractional-Order Chaotic Chemical Reaction Model via PD ζ Controller

Abstract

In this work, based on the earlier publications, we build a new fractional-order chemical reaction model. Computer simulations manifest that the fractional-order chemical reaction model presents chaotic behavior under a certain parameter condition. To eliminate the chaotic dynamical property, a suitable fractional-order ${\text{PD}}^{\zeta }$ controller with time delay is designed. Regarding the time delay as a bifurcation parameter, we set up a novel delay-independent stability and bifurcation criterion guaranteeing the stability and the creation of Hopf bifurcation of the controlled fractional-order chemical reaction model. The influence of time delay on the stability and Hopf bifurcation of the controlled fractional-order chemical reaction model is revealed. At last, numerical simulations are performed to sustain the rationality of the designed ${\text{PD}}^{\zeta }$ controller. The obtained conclusions of this work are completely novel and have immense application prospects in the chaos control of chemical reaction systems. Furthermore, the research idea can also be utilized to suppress the chaos of a lot of fractional-order chaotic models.