Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

Ying Yang, Daqing Jiang, Donal O’Regan and Ahmed Alsaedi
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Ying Yang: School of Mathematics, Changchun Normal University, Changchun 130000, China
Daqing Jiang: College of Science, China University of Petroleum(East China), Qingdao 266580, China
Donal O’Regan: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, EC5 855G Galway, Ireland
Ahmed Alsaedi: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2020, vol. 8, issue 5, 1-13

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 .

Keywords: Belousov-Zhabotinskii reaction model; lyapunov function; ergodicity; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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