Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Universal Bifurcation Chaos Theory and Its New Applications

Version 1 : Received: 5 May 2023 / Approved: 6 May 2023 / Online: 6 May 2023 (09:32:25 CEST)

A peer-reviewed article of this Preprint also exists.

Magnitskii, N.A. Universal Bifurcation Chaos Theory and Its New Applications. Mathematics 2023, 11, 2536. Magnitskii, N.A. Universal Bifurcation Chaos Theory and Its New Applications. Mathematics 2023, 11, 2536.

Abstract

In this work, an analytical and numerical analysis of the transition to chaos in five nonlinear systems of ordinary and partial differential equations, which are models of the autocatalytic chemical processes and the numbers of interacting populations, is carried out. It is analytically and numerically shown that in all considered systems of equations, further complication of the dynamics of solutions and the transition to chemical and biological turbulence is carried out in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic and homoclinic cascades of bifurcations of stable limit cycles. In this case, irregular (chaotic) attractors in all cases are exclusively singular attractors in the sense of the FShM theory.

Keywords

autocatalytic reactions; predator-prey models; hidden attractors; bifurcation cascades; chaos; singular attractors; chemical and biological turbulence; FShM theory

Subject

Computer Science and Mathematics, Applied Mathematics

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