
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 threedimensional system of nonlinear ordinary differential equations. The conditions for the birth of a limit cycle in the system as a result of AndronovHopf 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 FeigenbaumSharkovskyMagnitskii (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. 4953. DOI: 10.14357/20790279190205 References 1. Peng B., Scott S. K., Showalter K. Period Doubling and Chaos in a ThreeVariable Autocatalator. J. Phys. Chem. 1990, 94. P.52435246. 2. Gray P., Scott S. K. Autocatalytic Reactions in the Isothermal Continuous Stirred Tank Reactor. Chemical Engineering Science, 1984, 39 (6). P. 10871097. 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.133174. 6. Evstigneev N. M.,Magnitskii N.A. Numerical analysis of laminarturbulent bifurcation scenarios in KelvinHelmholtz and RayleighTaylor instabilities for compressible flow. Chapter in Turbulence. INTECH,2017.P.2959. 7. Magnitskii N.A. Bifurcation Theory of Dynamical Chaos. Chapter in Chaos Theory. INTECH, 2018, P. 197215.
