Self-Excited and Hidden Attractors Found Simultaneously in a Modified Chua's Circuit

Bao, Bocheng; Hu, Fengwei; Chen, Mo; Xu, Quan; Yu, Yajuan

doi:10.1142/s0218127415500753

Cited by 67 publications

(36 citation statements)

References 24 publications

(35 reference statements)

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“…There are even examples where all the three types of attractors coexist in phase space [1]. This striking dynamics has been previously observed in various dynamical systems including the Chua's circuit [2][3][4][5][6][7][8][9]. Chua's circuit is among the simplest electronic circuits characterized by chaos and many well-known nonlinear dynamic phenomena [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 77%

Complex Dynamics of the Chua’s Circuit System with Adjustable Symmetry and Nonlinearity: Multistability and Simple Circuit Realization

Tsafack¹,

Kengne²

2019

WJAP

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Background: Since the invention of Chua's circuit, numerous generalizations based on substitution of the nonlinear function have been reported. One of the generalizations is obtained by replacing the piecewise-linear with the cubic and/or quadratic polynomial. These nonlinearities are used to be implement using analog multipliers which are relatively expensive. In this realization we propose a different approach to synthetize both cubic and quadratic nonlinearities of empirical Chua's circuit. Methods: The idea is to use diodes, Opamps and resistors to derive a PWL approximation of the cubic and quadratic functions. To demonstrate some complex phenomena observed in the system using the fourth order Runge-Kutta numerical integration method with a very small integration step. The bifurcation diagram which is the plot of local maxima of the temporal trace of a system's coordinate as a function of the control parameter also constitutes an excellent tool for the study of dynamic systems. Results: The above mentioned standard nonlinear analysis tools have been exploited and it is found that the system with adjustable symmetry experiences a plethora of symmetric and asymmetric coexisting attractors. A particular feature of the system is related to the simplicity of the corresponding electronic analog circuit (no analog multiplier chip used to implement the cubic and quadratic nonlinearities). Conclusions: It is observed that the proposed Chua's circuit system is more flexible (both symmetric and asymmetric) and displays complex dynamics behaviors of symmetric and asymmetric coexisting attractors. Note that this striking dynamic can be exploited in encryption algorithms.

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Section: Introductionmentioning

confidence: 77%

Complex Dynamics of the Chua’s Circuit System with Adjustable Symmetry and Nonlinearity: Multistability and Simple Circuit Realization

Tsafack¹,

Kengne²

2019

WJAP

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“…the corresponding examples with phase-locked-loop based circuits in [40,41,42,43]). Observation of hidden Chua attractors in physical experiments is discussed, e.g., in [23,44,45,47,46].…”

Section: Resultsmentioning

confidence: 99%

Hidden and self-excited attractors in Chua circuit: synchronization and SPICE simulation

Kiseleva

Kudryashova

Kuznetsov

et al. 2017

International Journal of Parallel, Emergent and Distributed Sys

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Nowadays various chaotic secure communication systems based on synchronization of chaotic circuits are widely studied. To achieve synchronization, the control signal proportional to the difference between the circuits signals, adjust the state of one circuit. In this paper the synchronization of two Chua circuits is simulated in SPICE. It is shown that the choice of control signal is be not straightforward, especially in the case of multistability and hidden attractors.

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“…Further study of the hidden Chua attractors and their observation in physical experiments can be found, e.g. in Chen et al, 2015a;Bao et al, 2015a;Chen et al, 2015c,b;Zelinka, 2016;Bao et al, 2016;Menacer et al, 2016;Chen et al, 2017a;Rocha et al, 2017;Hlavacka & Guzan, 2017]. The synchronization of Chua circuits with hidden attractors is discussed, e.g.…”

Section: Introductionmentioning

confidence: 96%

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Stankevich

Kuznetsov

Леонов

et al. 2017

Int. J. Bifurcation Chaos

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Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.Comment: 20 pages, 11 figure

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Self-Excited and Hidden Attractors Found Simultaneously in a Modified Chua's Circuit

Cited by 67 publications

References 24 publications

Complex Dynamics of the Chua’s Circuit System with Adjustable Symmetry and Nonlinearity: Multistability and Simple Circuit Realization

Complex Dynamics of the Chua’s Circuit System with Adjustable Symmetry and Nonlinearity: Multistability and Simple Circuit Realization

Hidden and self-excited attractors in Chua circuit: synchronization and SPICE simulation

Scenario of the Birth of Hidden Attractors in the Chua Circuit

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