Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System

Abstract

Establishing suitable differential dynamical models to describe the real natural phenomenon in chemistry and physics has become a very hot topic in nowadays society. In this present research, we deal with a fractional-order chemical reaction system. Taking advantage of the fixed point theorem, we prove the existence and uniqueness of the fractional-order chemical reaction system. Using the inequality skill, we prove the non-negativeness of the fractional-order chemical reaction system. By applying a suitable function, we prove the uniform boundedness of the solution to the fractional-order chemical reaction system. With the aid of a hybrid controller including state feedback and parameter perturbation, we discuss the Hopf bifurcation anti-control issue of the fractional-order stable chemical reaction system. A novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation of the involved fractional-order stable chemical reaction system is set up. The study manifests that the delay in the hybrid controller plays a vital role in stabilizing the system and controlling the occurrence of Hopf bifurcation of the fractional-order stable chemical reaction system. In order to validate the derived key conclusions, MATLAB simulations are executed and bifurcation plots are given. The obtained results of this article have momentous theoretical guiding value in controlling the chemical compositions. The exploration idea can also be utilized to investigate the bifurcation control and bifurcation anti-control problems in lots of other fractional-order differential systems in numerous disciplines.