Codimension-One and Codimension-Two Bifurcations of a Fractional-Order Cubic Autocatalator Chemical Reaction System

Abstract

This article delves into an investigation of the dynamic behavior exhibited by a fractional order cubic autocatalator chemical reaction model. Specifically, our focus lies on exploring codimension-one bifurcations associated with period-doubling bifurcation and Neimark-Sacker bifurcation. Additionally, we undertake an analysis of codimension-two bifurcations linked to resonances of the types 1:2, 1:3, and 1:4. To achieve these outcomes, we employ the normal form method and bifurcation theory. The results are presented through comprehensive numerical simulations, encompassing visual representations such as phase portraits, two-parameter bifurcation diagrams, and maximum Lyapunov exponents diagrams. These simulations aptly examine the behavior of a system governed by two distinct parameters that vary within a three-dimensional space. Furthermore, the simulations effectively illustrate the theoretical findings while providing valuable insights into the underlying dynamics.