Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Abstract

In this current manuscript, we study a fractional-order modificatory hybrid optical model (FOMHO model). Experiments manifest that under appropriate parameter conditions, the fractional-order modificatory hybrid optical model will generate chaotic behavior. In order to eliminate the chaotic phenomenon of the (FOMHO model), we devise two different control techniques. First of all, a suitable delayed feedback controller is designed to control chaos in the (FOMHO model). A sufficient condition ensuring the stability and the occurrence of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is set up. Next, a suitable delayed mixed controller which includes state feedback and parameter perturbation is designed to suppress chaos in the (FOMHO model). A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is derived. In the end, software simulations are implemented to verify the accuracy of the devised controllers. The acquired results of this manuscript are completely new and have extremely vital significance in suppressing chaos in physics. Furthermore, the exploration idea can also be utilized to control chaos in many other differential chaotic dynamical models.