Abstract
In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.
Highlights
The theoretical analysis of repeated oscillation processes in open systems began in Lotkal [1,2]
The theory of dissipative structure argues that when the system is far from equilibrium state, that is, it is in the state of nonlinear and non-equilibrium, the disordered homogeneous state is not necessarily stable
It is necessary that the solutions of the stochastic model is positive in a chemical reaction model, so we prove the existence and uniqueness of the positive solution for model (5)
Summary
The theoretical analysis of repeated oscillation processes in open systems began in Lotkal [1,2]. Belousov observed the second example of oscillating chemical reactions in homogeneous solutions, i.e., oxidation of tetravalent-trivalent cerium ion coupled catalytic citric acid by potassium bromate. In 1969, Prigogine proposed the theory of dissipative structure, which clearly explains the reason for the occurrence of oscillation reaction This makes the B-Z reaction back to the focus of the study. B bromate ion oxidate the metal ions, and generate bromine Such oscillation can sustain thousands of times in the closed system, and the reaction process does not need to add the reactants. This kind of reaction provides great convenience for the study of the chemical wave.
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