Journal ArticleDOI
Simple chaotic flows with a line equilibrium
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In this article, the authors used a systematic computer search to find chaotic flows with quadratic nonlinearities that have the unusual feature of having a line equilibrium, which is called hidden attractor chaotic flow.Abstract:
Using a systematic computer search, nine simple chaotic flows with quadratic nonlinearities were found that have the unusual feature of having a line equilibrium. Such systems belong to a newly introduced category of chaotic systems with hidden attractors that are important and potentially problematic in engineering applications.read more
Citations
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Hidden attractors in dynamical systems
Dawid Dudkowski,Sajad Jafari,Tomasz Kapitaniak,Nikolay Kuznetsov,Nikolay Kuznetsov,Gennady A. Leonov,Awadhesh Prasad +6 more
TL;DR: In this paper, the authors discuss the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations, and also describe numerical methods which allow identification of the hidden attractor.
Journal ArticleDOI
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
TL;DR: In this paper, a self-excited and hidden attractor for a Lorenz-like system derived from the well-known Glukhovsky-Dolghansky and Rabinovich systems was analyzed.
Journal ArticleDOI
Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit
TL;DR: In this article, the multiple attractors with different initial states are revealed and with the dimensionless system equations, complex dynamics with various initial conditions are further discussed and theoretical derivation results indicate that the normalized memristive Chua's system has two stable nonzero saddle-foci in globally adjusting normalized parameter region and exhibits the unusual and striking dynamical behavior of multiple attractor with multistability.
Journal ArticleDOI
Recent new examples of hidden attractors
TL;DR: In this paper, the authors present several types of rare chaotic flows with hidden attractors, including those with no equilibrium, rare flows with a line of equilibrium points, and rare flow with a stable equilibrium.
Journal ArticleDOI
A novel memristive neural network with hidden attractors and its circuitry implementation
TL;DR: Interestingly, the memristive neural network can generate hyperchaotic attractors without the presence of equilibrium points and circuital implementation of such memristives is presented to show its feasibility.
References
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Journal ArticleDOI
Some simple chaotic flows.
TL;DR: A systematic examination of general three-dimensional autonomous ODE with quadratic nonlinearities has uncovered 19 distinct simple examples of chaotic flows with either five terms and two non-linearities or six terms and one nonlinearity as mentioned in this paper.
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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
TL;DR: The problem of investigating hidden oscillations arose in the second part of Hilbert's 16th problem (1900), and the first nontrivial results were obtained in Bautin's works, which revealed no similar transient processes leading to such attractors.
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Localization of hidden Chuaʼs attractors
TL;DR: In this article, the authors proposed to use a special analytical-numerical algorithm to locate hidden attractors of Chua's circuit. But this algorithm does not consider the hidden attractor of the neighborhood of equilibrium.
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Hidden attractor in smooth Chua systems
Gennady A. Leonov,Gennady A. Leonov,Nikolay Kuznetsov,Nikolay Kuznetsov,V. I. Vagaitsev,V. I. Vagaitsev +5 more
TL;DR: In this paper, it was shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems with a smooth characteristic of nonlinear element.
Journal ArticleDOI
Elementary quadratic chaotic flows with no equilibria
TL;DR: In this article, three methods are used to produce a catalog of seventeen elementary three-dimensional chaotic flows with quadratic nonlinearities that have the unusual feature of lacking any equilibrium points.