Canards Oscillations, Noise-Induced Splitting of Cycles and Transition to Chaos in Thermochemical Kinetics

Irina Bashkirtseva (), Grigoriy Ivanenko, Dmitrii Mordovskikh and Lev Ryashko
Additional contact information
Irina Bashkirtseva: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia
Grigoriy Ivanenko: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia
Dmitrii Mordovskikh: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia
Lev Ryashko: Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia

Mathematics, 2023, vol. 11, issue 8, 1-9

Abstract: We study how noise generates complex oscillatory regimes in the nonlinear thermochemical kinetics. In this study, the basic mathematical Zeldovich–Semenov model is used as a deterministic skeleton. We investigate the stochastic version of this model that takes into account multiplicative random fluctuations of temperature. In our study, we use direct numerical simulation of stochastic solutions with the subsequent statistical analysis of probability densities and Lyapunov exponents. In the parametric zone of Canard cycles, qualitative effects caused by random noise are identified and investigated. Stochastic P -bifurcations corresponding to noise-induced splitting of Canard oscillations are parametrically described. It is shown that such P -bifurcations are associated with splitting of both amplitudes and frequencies. Studying stochastic D -bifurcations, we localized the rather narrow parameter zone where transitions from order to chaos occur.

Keywords: thermochemical oscillations; Canard cycles; stochastic bifurcations; stochastic splitting; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/8/1918/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/8/1918/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:8:p:1918-:d:1126870

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().