Control of multistability in hidden attractors

Sharma, Pradeep; Shrimali, Manish Dev; Prasad, Awadhesh; Kuznetsov, Nikolay V.; Леонов, Г. А.

doi:10.1140/epjst/e2015-02474-y

Cited by 193 publications

(62 citation statements)

References 25 publications

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“…Extreme multistability is a fantastic kind of multistability, which makes a nonlinear dynamical circuit or system supply great flexibility for its potential uses in chaos-based engineering applications [10][11][12], but also raises new challenges for its control of the existing multiple stable states [11][12][13][14]. Generally, multistability is confirmed in hardware experiments by randomly switching on and off experimental circuit supplies [9,[15][16][17][18][19][20][21] or by MATLAB numerical or PSPICE/PSIM circuit simulations [4][5][6][7][8][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

et al. 2018

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This paper investigates extreme multistability and its controllability for an ideal voltage-controlled memristor emulator-based canonical Chua's circuit. With the voltage-current model, the initial condition-dependent extreme multistability is explored through analyzing the stability distribution of line equilibrium point and then the coexisting infinitely many attractors are numerically uncovered in such a memristive circuit by the attraction basin and phase portraits. Furthermore, based on the accurate constitutive relation of the memristor emulator, a set of incremental flux-charge describing equations for the memristor-based canonical Chua's circuit are formulated and a dimensionality reduction model is thus established. As a result, the initial condition-dependent dynamics in the voltage-current domain is converted into the system parameter-associated dynamics in the flux-charge domain, which is confirmed by numerical simulations and circuit simulations. Therefore, a controllable strategy for extreme multistability can be expediently implemented, which is greatly significant for seeking chaos-based engineering applications of multistable memristive circuits.

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Section: Introductionmentioning

confidence: 99%

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

et al. 2018

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“…It is worth noting that systems with stable equilibria are systems with 'hidden attractors' [26][27][28][29]. Hidden attractors have received considerable attention recently because of their roles in theoretical and practical problems [30][31][32][33][34][35][36][37][38]. Different definitions and main properties of fractional calculus have been reported in the literature [47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

A fractional-order form of a system with stable equilibria and its synchronization

et al. 2018

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There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes.

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“…The second one is self-excited attractor. An attractor is called self-excited if its basin of attraction is associated with an unstable equilibrium [19][20][21]. In the case of chaotic attractors in systems with a stable equilibrium, at least there are two attractors simultaneously (strange attractor and stable equilibrium attractor).…”

Section: Introductionmentioning

confidence: 99%

A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

Khalaf¹,

Kapitaniak²,

Rajagopal³

et al. 2018

Open Physics

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This paper proposes a new three-dimensional chaotic ow with one stable equilibrium. Dynamical properties of this system are investigated. The system has a chaotic attractor coexisting with a stable equilibrium. Thus the chaotic attractor is hidden. Basin of attractions shows the tangle of di erent attractors. Also, some complexity measures of the system such as Lyapunov exponent and entropy will are analyzed. We show that the Kolmogorov-Sinai Entropy shows more accurate results in comparison with Shanon Entropy.

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Control of multistability in hidden attractors

Cited by 193 publications

References 25 publications

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

A fractional-order form of a system with stable equilibria and its synchronization

A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

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