Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations

Abstract

We consider a system of fractional delayed differential equations. The ordinary differential version of the system without delay is introduced in the Lengyel-Epstein reaction-diffusion system. We evaluate the system with and without delay and explore the stability of the unique positive equilibrium. We also prove the existence of Hopf bifurcation for both cases. Furthermore, the impacts of Caputo fractional order parameter and time delay parameter on the dynamics of the system are investigated with numerical simulations. It is also concluded that for different values of time delay parameter, the decreament of the Caputo fractional order parameter has opposite effects on the system in terms of stability.

Keywords

• caputo fractional derivative
• fractional delayed differential equations
• hopf bifurcation
• lengyel-epstein equation