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Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model
- Source :
- Mathematics, Volume 8, Issue 5, Mathematics, Vol 8, Iss 663, p 663 (2020)
- Publication Year :
- 2020
- Publisher :
- Multidisciplinary Digital Publishing Institute, 2020.
-
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&rsquo<br />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.
- Subjects :
- Lyapunov function
0209 industrial biotechnology
Stochastic modelling
General Mathematics
02 engineering and technology
01 natural sciences
symbols.namesake
020901 industrial engineering & automation
Computer Science::Emerging Technologies
0103 physical sciences
Computer Science (miscellaneous)
Ergodic theory
Applied mathematics
Uniqueness
Engineering (miscellaneous)
lyapunov function
Mathematics
Belousov-Zhabotinskii reaction model
Stationary distribution
010304 chemical physics
Chemical reaction model
lcsh:Mathematics
Ergodicity
lcsh:QA1-939
Nonlinear Sciences::Cellular Automata and Lattice Gases
stationary distribution
Ordinary differential equation
symbols
ergodicity
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....a4577a50667aa7c585476ad7fcd5443b
- Full Text :
- https://doi.org/10.3390/math8050663