Scenario of the Birth of Hidden Attractors in the Chua Circuit

Abstract

Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.Comment: 20 pages, 11 figure

Coexisting hidden attractors in a 5D segmented disc dynamo with three types of equilibria

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In Memoriam: Gennady Alekseevich Leonov

“…Consequently, the Fishing principle has provided mathematicians with a universal tool for analytically proving the existence of homoclinic orbits in a number of well-known dynamical systems. Last, but not least, the notion of hidden attractors and the development of new mathematical methods for investigating such attractors in classic dynamical systems [Leonov & Kuznetsov, 2013;Leonov et al, 2015b;Kuznetsov et al, 2018] have attracted a great deal of interest from researchers in various fields, especially mathematicians, engineers, and physicists [Bragin et al, 2011;Sharma et al, 2015aSharma et al, , 2015bDudkowski et al, 2016;Chen et al, 2017;Stankevich et al, 2017]. Largely due to the discovery of hidden attractors in dynamical systems, Gennady Leonov and his former doctoral student Nikolay V. Kuznetsov were proclaimed as the Highly Cited Researchers in the Russian Federation twice over two consecutive years (2016-2017) by Clarivate Analytics.…”

The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension

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