New Ways of Transition to Deterministic Chaos in Nonideal Oscillating Systems

Олександр Юрійович Швець, Василь Олександрович Сіренко

Abstract


We considered nonideal dynamical system with a five-dimensional phase space. Questions of occurrence of deterministic chaos in such systems are investigated. By using the previously developed by the authors the technique of computer simulation of deterministic chaos, we discovered and described a number of new scenarios of transition to deterministic chaos. In this research analyzed in detail the phase portraits, signatures of spectrum of Lyapunov characteristic exponents and distribution of the invariant measure in various regular and chaotic attractors. In particular, there is found the transition to chaos by the scenario of generalized intermittency with two laminar phases. Succeed to identify the transition to chaos, which begins by the Feigenbaum scenario and ends through intermittency. The role of symmetry of attractors in such transitions is explored. Identified the transitions to chaos, by scenario of the generalized intermittency, with two coarse-grained laminar phases. Also managed to find the scenario of generalized intermittency, in which taken place the transition from hyper-attractor of one type to another type of hyper-attractor.

Keywords


Nonideal dynamical system; Chaotic attractor; Scenarios of transitions to chaos

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References


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DOI: https://doi.org/10.20535/1810-0546.2015.1.88164

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