Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems

Chen, G.; Kuznetsov, Nikolay V.; Леонов, Г. А.; Mokaev, Timur N.

doi:10.1142/s0218127417501152

Cited by 58 publications

(34 citation statements)

References 43 publications

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“…Definition 2. [73,74] A transient chaotic set is called a hidden transient chaotic set if it does not involve and attract trajectories from a small neighborhood of equilibria; otherwise, it is called self-excited.…”

Section: Attractors and Transient Chaosmentioning

confidence: 99%

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

Kuznetsov¹,

Леонов²,

Mokaev³

et al. 2018

Nonlinear Dyn

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151

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The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor. The hidden attractor in this system can be localized by analytical/numerical methods based on the continuation and perpetual points. The concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of exact Lyapunov dimension are discussed. A comparative survey on the computation of the finite-time Lyapunov exponents and dimension by different algorithms is presented. An adaptive algorithm for studying the dynamics of the finite-time Lyapunov dimension is suggested. Various estimates of the finite-time Lya-

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Section: Attractors and Transient Chaosmentioning

confidence: 99%

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

Kuznetsov¹,

Леонов²,

Mokaev³

et al. 2018

Nonlinear Dyn

Self Cite

151

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“…Several classes of chaotic autonomous systems with hidden attractors were reviewed in [12], showing that there exist several main groups of hidden attractors: (i) rare flows with no equilibrium [23], (ii) rare flows with a line of equilibrium points [21], and (iii) rare flows with one and only one equilibrium, which is stable [24], and so on. While hidden attractors have been found from various Lorenz-like systems [2], the existence of hidden attractors in the Lorenz and Chen systems is still an open problem.…”

Section: Xu Zhang and Guanrong Chenmentioning

confidence: 99%

Polynomial maps with hidden complex dynamics

Zhang

Chen²

2019

Discrete &Amp; Continuous Dynamical Systems - B

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The dynamics of a class of one-dimensional polynomial maps are studied, and interesting dynamics are observed under certain conditions: the existence of periodic points with even periods except for one fixed point; the coexistence of two attractors, an attracting fixed point and a hidden attractor; the existence of a double period-doubling bifurcation, which is different from the classical period-doubling bifurcation of the Logistic map; the existence of Li-Yorke chaos. Furthermore, based on this one-dimensional map, the corresponding generalized Hénon map is investigated, and some interesting dynamics are found for certain parameter values: the coexistence of an attracting fixed point and a hidden attractor; the existence of Smale horseshoe for a subshift of finite type and also Li-Yorke chaos.

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“…According to the definition of hidden attractors, the system's attractors belong to hidden attractors. Its basin of attraction does not contain neighborhoods of equilibria [32,33].…”

Section: Model Of the New Chaotic Systemmentioning

confidence: 99%

Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors

Liu

Zhang

et al. 2019

Entropy

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This paper presents a new no-equilibrium 4-D hyperchaotic multistable system with coexisting hidden attractors. One prominent feature is that by varying the system parameter or initial value, the system can generate several nonlinear complex attractors: periodic, quasiperiodic, multiple topology chaotic, and hyperchaotic. The dynamics and complexity of the proposed system were investigated through Lyapunov exponents (LEs), a bifurcation diagram, a Poincaré map, and spectral entropy (SE). The simulation and calculation results show that the proposed multistable system has very rich and complex hidden dynamic characteristics. Additionally, the circuit of the chaotic system is designed to verify the physical realizability of the system. This study provides new insights into uncovering the dynamic characteristics of the coexisting hidden attractors system and provides a new choice for nonlinear control or chaotic secure communication technology.

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Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems

Cited by 58 publications

References 43 publications

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

Polynomial maps with hidden complex dynamics

Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors

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