Journal ArticleDOI
Constructing a Novel No-Equilibrium Chaotic System
TLDR
A new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium is introduced.Abstract:
This paper introduces a new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. The dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincare map and period-doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without equilibria are also proposed by applying the presented methodology.read more
Citations
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Journal ArticleDOI
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
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
Hidden Bursting Firings and Bifurcation Mechanisms in Memristive Neuron Model With Threshold Electromagnetic Induction
TL;DR: A threshold flux-controlled memristor is presented and its frequency-dependent pinched hysteresis loops are examined, validating the physical mechanism of biological neuron and the reliability of electronic neuron.
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
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
Journal ArticleDOI
An equation for continuous chaos
TL;DR: A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable as mentioned in this paper, which allows for a "folded" Poincare map (horseshoe map).
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Yet another chaotic attractor
Guanrong Chen,Tetsushi Ueta +1 more
TL;DR: In this paper, the authors reported the finding of a chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.
Journal ArticleDOI
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.