Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction

Lev Ryashko and Irina Bashkirtseva
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Lev Ryashko: Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, Russia
Irina Bashkirtseva: Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, Russia

Mathematics, 2022, vol. 10, issue 6, 1-11

Abstract: The Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and large amplitudes. In the parametric analysis of the stochastic excitement, we use the analytical method of confidence domains based on the stochastic sensitivity technique. Analyzing a mutual arrangement of the confidence ellipses and separatrices, we estimate the critical intensity of the noise that causes the excitation. The phenomena of stochastic P-bifurcations and coherence resonances are discovered and studied by probability density functions and the statistics of interspike intervals.

Keywords: thermochemical reaction; bifurcations; random disturbances; stochastic sensitivity; excitement; coherence resonance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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