Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Motivated by the increasingly important role of mathematical modeling and computer-aided analysis in engineering applications, we consider the problem of the mathematical modeling and computer-aided analysis of complex stochastic processes in thermo-kinetics. We study a mathematical model of the dyn...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-10, Vol.11 (20), p.4302
Main Authors: Bashkirtseva, Irina, Pavletsov, Makar, Perevalova, Tatyana, Ryashko, Lev
Format: Article
Language:English
Subjects:
Autocatalysis
autocatalytic trigger
Bifurcations
Chemical tests and reagents
Critical phenomena
Direct numerical simulation
Equilibrium
Mathematical models
noise-induced transitions
Numerical analysis
Reagents
Simulation
Simulation methods
Stochastic processes
stochastic sensitivity
thermo-kinetic model
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Summary:Motivated by the increasingly important role of mathematical modeling and computer-aided analysis in engineering applications, we consider the problem of the mathematical modeling and computer-aided analysis of complex stochastic processes in thermo-kinetics. We study a mathematical model of the dynamic interaction of reagent concentration and temperature in autocatalysis. For the deterministic variant of this model, mono- and bistability parameter zones as well as local and global bifurcations are revealed, and we show how random multiplicative disturbances can deform coexisting equilibrium regimes. In a study of noise-induced transitions, we apply direct numerical simulation and an analytical approach based on the stochastic sensitivity technique. Two variants of bistability with different scenarios of stochastic transformations are studied and compared.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11204302