Qualitative Behavior of a Chemical Reaction System With Fractional Derivatives

Chemical reactions can be successfully investigated using fractional differential equations. This work aims to explore new outcomes such as fixed points, local stability, types of bifurcations, limit cycles for a fractional-order chemical reaction system which arises in chemical reactions. The equilibrium point of this system is presented and method of linearization is successfully implemented to analyze the asymptotic behavior of solutions about the positive equilibrium point. Taking advantage of the bifurcation theory, we examine the existence of a period-doubling bifurcation and a Neimark–Sacker bifurcation. We find that this system undergoes period-doubling and Neimark–Sacker bifurcations under some specific values of bifurcation parameter. The maximum Lyapunov characteristic exponents are shown. We present some 2D diagrams for the phase portraits, local stability, closed invariant curves, types of bifurcations, and the maximum Lyapunov exponents to ensure the chaotic behavior of the considered model. The used techniques can be applied to deal with other high-order models.