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Localization of hidden Chuaʼs attractors
Abstract The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to useExpand
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Time-Varying Linearization and the Perron Effects
TLDR
In the present survey, the contemporary state of the art of the problem of the justification of nonstationary linearizations is presented. Expand
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Hidden attractors in Dynamical Systems. From Hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits
TLDR
From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Expand
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Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits
An algorithm for searching hidden oscillations in dynamic systems is developed to help solve the Aizerman’s, Kalman’s and Markus-Yamabe’s conjectures well-known in control theory. The first step ofExpand
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Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory
TLDR
In this survey an attempt is made to discuss and fill some of the gaps identified between mathematical control theory, the theory of dynamical systems and the engineering practice of phase-locked loops. Expand
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Algorithm for localizing Chua attractors based on the harmonic linearization method
The method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden attractors of control systems. In the presentExpand
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Hidden attractors in dynamical systems
Abstract Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system isExpand
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Hidden attractor in smooth Chua systems
Abstract The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50–60s of the 20th century in automatic control systemsExpand
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Hidden oscillations in dynamical systems
TLDR
The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. Expand
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The Lyapunov dimension and its estimation via the Leonov method
Abstract Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, proposed by G.A. Leonov in 1991. The Leonov method isExpand
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