Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial

Teng, Lin; Iu, Herbert Ho-Ching; Wang, Xingyuan; Wang, Xiukun

doi:10.1007/s11071-014-1286-4

Cited by 94 publications

(72 citation statements)

References 20 publications

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“…Theoretical analyses, numerical simulations and circuit experiments consistently indicate that such memristor-based systems can exhibit complex dynamical behaviours including various bifurcation [1][2][3][4][5][6][7][8][9][10][11][12], chaos [1][2][3][4][5][6][7][8][9][10][11][12], hyperchaos [12][13][14], coexistence of attractors [15], transient dynamical behaviors [16], and initial state dependent dynamical behaviors [17]. Moreover, several fractional-order memristor-based systems and their dynamical behaviors are presented in [9,18,19]. However, the above-mentioned systems are all real systems, and to our best knowledge, there are no reports of memristor-based complex systems.…”

Section: Introductionmentioning

confidence: 91%

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

Wang

Zhou

2015

Entropy

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Abstract:The aim of this paper is to introduce and investigate a novel complex Lorenz system with a flux-controlled memristor, and to realize its synchronization. The system has an infinite number of stable and unstable equilibrium points, and can generate abundant dynamical behaviors with different parameters and initial conditions, such as limit cycle, torus, chaos, transient phenomena, etc., which are explored by means of time-domain waveforms, phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, an active controller is designed to achieve modified projective synchronization (MPS) of this system based on Lyapunov stability theory. The corresponding numerical simulations agree well with the theoretical analysis, and demonstrate that the response system is asymptotically synchronized with the drive system within a short time.

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Section: Introductionmentioning

confidence: 91%

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

Wang

Zhou

2015

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“…In this section, according to the charge-controlled memristor characterized by a fourth degree polynomial function in [19], the memristor in System (7) is replaced with the new flux-controlled memristor characterized by a quartic nonlinearity. Additionally, we can get the following equations of the fractional-order memristor-based Lorenz system with a quartic nonlinearity as:…”

Section: Fractional-order Lorenz System With the Flux-controlled Memrmentioning

confidence: 99%

“…In [15][16][17][18], flux-controlled memristors characterized by a smooth continuous cubic nonlinearity are presented. Furthermore, research has been done on the charge-controlled memristor characterized by a fourth degree polynomial function [19]. Compared to classical integer-order models, the fractional derivative provides a wonderful implement for describing the memory and hereditary properties of all kinds of materials and processes.…”

Section: Introductionmentioning

confidence: 99%

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Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems

Huang

2014

Entropy

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In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams.Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.

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“…On the other hand, the chaotic vibration signal by employing the memristor can be applied to many fields such as secure communication and aerospace industry. So researchers began to focus on the design and realization of memristive chaotic circuit [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In these literatures, only one memristor was applied in an independent circuit, and the dynamic characteristics of memristive chaotic system are related to the initial state of memristor, including unique nonlinear physics phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Characteristic Analysis of Fractional‐Order 4D Hyperchaotic Memristive Circuit

Mou

Sun

Wang

et al. 2017

Mathematical Problems in Engineering

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Dynamical behaviors of the 4D hyperchaotic memristive circuit are analyzed with the system parameter. Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical solution of fractional-order 4D hyperchaotic memristive circuit is investigated. The distribution of stable and unstable regions of the fractional-order 4D hyperchaotic memristive circuit is determined, and dynamical characteristics are studied by phase portraits, Lyapunov exponents spectrum, and bifurcation diagram. Complexities are calculated by employing the spectral entropy (SE) algorithm and C 0 algorithm. Complexity results are consistent with that of the bifurcation diagrams, and this means that complexity can also reflect the dynamic characteristics of a chaotic system. Results of this paper provide a theoretical and experimental basis for the application of fractionalorder 4D hyperchaotic memristive circuit in the field of encryption and secure communication.

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Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial

Cited by 94 publications

References 20 publications

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems

Characteristic Analysis of Fractional‐Order 4D Hyperchaotic Memristive Circuit

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