Estimation of efficiency of production and infrastructure subsystems
Macrosystem dynamics
N.A. Magnitskii Bifurcations and chaos in one model of an autocatalytic chemical process with feedback
MATHEMATICAL MODELING
System analysis in medicine and biology
N.A. Magnitskii Bifurcations and chaos in one model of an autocatalytic chemical process with feedback

Abstract.

The paper presents an analytical and numerical analysis of the transition to chaos in the model of an autocatalytic chemical process with feedback, which is a three-dimensional system of nonlinear ordinary differential equations. The conditions for the birth of a limit cycle in the system as a result of Andronov-Hopf bifurcation are found. It is shown numerically that the transition to chaos in the system is carried out in full accordance with the universal bifurcation theory of Feigenbaum-Sharkovsky-Magnitskii (FShM) through the subharmonic and initial stage of the homoclinic cascades of bifurcations of stable limit cycles.

Keywords:

autocatalytic reactions, cascades of bifurcations, attractors, chaos.

PP. 49-53.

DOI: 10.14357/20790279190205

References

1. Peng B., Scott S. K., Showalter K. Period Doubling and Chaos in a Three-Variable Autocatalator. J. Phys. Chem. 1990, 94. P.5243-5246.
2. Gray P., Scott S. K. Autocatalytic Reactions in the Isothermal Continuous Stirred Tank Reactor. Chemical Engineering Science, 1984, 39 (6). P. 1087-1097.
3. Magnitskii N.A., Sidorov S.V. New methods for chaotic dynamics (monograph). Singapore: World Scientific, 2006. 363 p.
4. Magnitskii N.A. Teoriya dinamicheskogo khaosa [Theory of dynamical chaos]. M.: Lenand, 2011. 320s.
5. Magnitskii N.A. Universality of Transition to Chaos in All Kinds of Nonlinear Differential Equations. Chapter in Nonlinearity, Bifurcation and Chaos – Theory and Applications. INTECH, 2012.P.133-174.
6. Evstigneev N. M.,Magnitskii N.A. Numerical analysis of laminar-turbulent bifurcation scenarios in Kelvin-Helmholtz and Rayleigh-Taylor instabilities for compressible flow. Chapter in Turbulence. INTECH,2017.P.29-59.
7. Magnitskii N.A. Bifurcation Theory of Dynamical Chaos. Chapter in Chaos Theory. INTECH, 2018, P. 197-215.
 

 

2023-73-4
2023-73-3
2023-73-2
2023-73-1

© ФИЦ ИУ РАН 2008-2018. Создание сайта "РосИнтернет технологии".