Localization of hidden Chuaʼs attractors

By Gennady A. Leonov, Nikolay V. Kuznetsov, Vladimir I. Vagaitsev. 2011

614 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2d4b80460d460c026639a13aba073e1ea390581b

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Hidden attractor in smooth Chua systems (2012, methodology): “By (10) and thematrix S (which can be found using [22]) for the transformation of system (14) to the form (6), one can obtain the initial data, namely”
Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor (2014, background): “, localization of hidden oscillations in various modifications of electrical Chua circuits [33,34,36,50–52], counterexamples to Aizerman conjecture and Kalman conjecture on absolute stability of nonlinear control systems [35,44,45], phase-locked loops [48,49], and aircraft control systems [5,6].”
Hidden oscillations in dynamical systems (2011, methodology): “However there are attractors of another type [25]: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria.”
Simple Chaotic flows with One Stable equilibrium (2013, background): “Recent research has involved categorizing periodic and chaotic attractors as either self-excited or hidden [Kuznetsov et al., 2010, 2011a, 2011b; Leonov & Kuznetsov, 2011a, 2011b, 2013a, 2013b; Leonov et al., 2011a, 2011b, 2012].”
Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit (2015, background): “These nonlinear dynamical behaviors are conventionally excited from unstable equilibriumpoints,while newkinds of attractors, called as hidden attractors [17], have been found in classical Chua’s circuit, whose generations have nothing to do with any unstable equilibrium points [17–19].”
Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits (2011, background): “Such algorithms help find and localize hidden strange attractors [ 88 ] as well as hidden periodic oscillations.”
Simple chaotic flows with a line equilibrium (2013, methodology): “From a computational point of view this allows one to use a numerical method in which a trajectory started from a point on the unstable manifold in the neighborhood of an unstable equilibrium, reaches an attractor and identifies it [7].”