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

摘要

This paper examines the dynamical analysis of the Lengyel-Epstein system with a discrete delay in detail. Under the assumption that the unique positive equilibrium of the model is locally asymptotically stable in the absence of the delay, the effect of the increase of delay on the stability of the unique positive equilibrium is analyzed in detail. It is found that under suitable conditions on the other parameters, the delay doesn't affect the stability of the equilibrium, namely, the equilibrium is absolutely stable while under the other conditions on the other parameters, the equilibrium will become ultimately unstable after passing through multiple stability switches and Hopf bifurcations at some certain critical values of delay. Particularly, 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. (c) 2020 Elsevier Inc. All rights reserved.