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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.

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

This paper is devoted to investigate the problem of controlling chaos in a 3D ratio-dependent food chain system. Time-delayed feedback control method is applied to suppress chaos to unstable equilibria or unstable periodic orbits. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Some numerical simulations are presented to support theoretical predictions. Finally, main conclusions are drawn. [ABSTRACT FROM AUTHOR]