Hopf and Turing bifurcations analysis for the modified Lengyel–Epstein system

Abstract

In this paper, we investigate the dynamics for the modified Lengyel–Epstein system of the photosensitive CDIMA reaction. Specifically, considering the impact of illumination intensity, more limit cycles are discovered in the modified Lengyel–Epstein system compared to the original model. This enhancement not only enriches the dynamical phenomena but also indicates the system’s heightened sensitivity to the light intensity. By the center manifold theorem and normal form theory, we achieve the existence of Hopf bifurcation for both the corresponding ODE system and PDE system. Moreover, we provide some conditions for Turing instability, Turing bifurcation, spatially homogeneous and inhomogeneous Hopf bifurcation and Turing–Hopf bifurcation. Finally, we discuss the effect of illumination intensity for dynamical behavior of the modified Lengyel–Epstein system.