Abstract
In this paper, a Lengyel–Epstein model with two delays is proposed and considered. By choosing the different delay as a parameter, the stability and Hopf bifurcation of the system under different situations are investigated in detail by using the linear stability method. Furthermore, the sufficient conditions for the stability of the equilibrium and the Hopf conditions are obtained. In addition, the explicit formula determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained with the normal form theory and the center manifold theorem to delay differential equations. Some numerical examples and simulation results are also conducted at the end of this paper to validate the developed theories.
Highlights
It is of great significance to study the dynamical behaviors of chemical reaction models to understand the reaction mechanism and evolution law of the reaction process of reactants
In the past few decades, the dynamic behavior of the time-delay model has been widely concerned in many fields, which is inseparable from its biological and physical significance. e research on the dynamics of delay differential equations has always been the focus of attention in various fields
It is especially widely used in chemistry. e main reason is that the chemical reaction of the system with a particular input is often not immediate but delayed, and the system has different time delays for a chemical reaction with different inputs. erefore, it is necessary to analyze the dynamical behaviors of the system with multiple delays
Summary
It is of great significance to study the dynamical behaviors of chemical reaction models to understand the reaction mechanism and evolution law of the reaction process of reactants. There are many chemical reaction functional differential equations in nature, so it is of great practical significance to study the existence, stability, and Hopf bifurcation of periodic solutions of these functional differential equations in the field of chemistry. With the maturity of the biological mathematics theory, researchers began to realize the importance of time delay in chemical reaction systems These models (2)–(5) discussed above are based on the hypothesis that the delay effect is a single activator or inhibitor alone.
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