Multiple stability switches and Hopf bifurcations induced by the delay in a Lengyel-Epstein chemical reaction system

Highlights：

• This paper is concerned with the detailed dynamics analysis of the Lengyel-Epstein system with a discrete delay.

• Under the assumption that the positive equilibrium of the model is locally asymptotically stable in the absence of delay, the effect of the increase of delay on the stability of the unique positive equilibrium is analyzed in detail.

• The phenomenon that the equilibrium becomes ultimately unstable after passing through multiple stability switches and Hopf bifurcations at some certain critical values of delay is found.

• By means of the normal form method and the center manifold reduction for retarded functional differential equations, the explicit formulae determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions are obtained.

• To verify our theoretical conclusions, some numerical simulations for specific examples are also included at the end of this article.