Behavior of Dynamical Systems in the Regime of Transient Chaos
TLDR
In this article, the transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered and it is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control parameters by the presence of "nonregular" regions, the number of which increases with the critical parameter.Abstract:
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control parameters by the presence of “nonregular” regions, the number of which increases with the critical parameter. A possible mechanism of this effect is discussed.read more
Citations
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A simple memristor chaotic circuit with complex dynamics
TL;DR: Some novel transient transition behaviors with different time scales are found in the memristor circuit, both theoretically and numerically.
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Transient chaos in smooth memristor oscillator
TL;DR: In this article, a new smooth memristor oscillator was derived from Chua's oscillator by replacing the diode with a flux-controlled memristors and a negative conductance.
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A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system
TL;DR: In this paper, a 4D smooth quadratic autonomous chaotic system is presented, which can present periodic orbit, chaos, and hyper-chaos under the conditions on different parameters.
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Hidden transient chaotic attractors of Rabinovich–Fabrikant system
TL;DR: In this article, it was shown that the Rabinovich-fabrikant (RF) system admits self-excited and hidden chaotic attractors, such as virtual saddles.
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Hidden transient chaotic attractors of Rabinovich-Fabrikant system
TL;DR: In this article, it was shown that the Rabinovich-fabrikant (RF) system admits self-excited and hidden chaotic attractors, and a pair of symmetric transient Hidden Chaotic Entanglement (HCE) attractors.
References
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Journal ArticleDOI
A Two-dimensional Mapping with a Strange Attractor
TL;DR: In this article, the same properties can be observed in a simple mapping of the plane defined by: \({x i + 1}} = {y_i} + 1 - ax_i^2,{y i+ 1} = b{x_i}\).
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Practical Numerical Algorithms for Chaotic Systems
Thomas S. Parker,Leon O. Chua +1 more
TL;DR: The goal of this book is to present an elementary introduction on chaotic systems for the non-specialist, and to present and extensive package of computer algorithms for simulating and characterizing chaotic phenomena.
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Chaotic attractors in crisis
TL;DR: In this article, the occurrence of sudden qualitative changes of chaotic (or "turbulent") dynamics is discussed and illustrated within the context of the one-dimensional quadratic map, and the cause and properties of these phenomena are investigated.
Journal ArticleDOI
Critical exponents for crisis-induced intermittency
TL;DR: Three types of changes that attractors can undergo as a system parameter is varied are considered, which are termed crises, where one (or more) chaotic attractors merge to form a single chaotic attractor and the merged attractor can be larger in phase-space extent than the union of the attractors before the change.
Journal ArticleDOI
Different ways to turbulence in dissipative dynamical systems
Paul Manneville,Yves Pomeau +1 more
TL;DR: In this paper, a semi-quantitative interpretation of these processes and their relation with the different transitions to turbulence observed experimentally are discussed. But their results are restricted to the case where σ = 10, b = 8 3 and r r = 145 and r = 148.
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