Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode

Wang, Ning; Li, Chengqing; Bao, Han; Chen, Mo; Bao, Bocheng

doi:10.1109/tcsi.2019.2933365

Cited by 146 publications

(59 citation statements)

References 55 publications

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“…The authors, in their investigation, analyze the impact of the fractional-order derivative into Chua's electrical circuit. In [6], Wang et al investigate on generating multiscroll Chua's attractors using the simplified piecewise-linear Chua's diode. In [7,13], Petras presents the control problem in the context of the fractional Chua's electrical circuit.…”

Section: Introductionmentioning

confidence: 99%

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

Sene¹

2021

Rev. Mex. Fís.

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This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

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Section: Introductionmentioning

confidence: 99%

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

Sene¹

2021

Rev. Mex. Fís.

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“…Chaotic systems have long been a subject of concern in academic and industrial fields [ 1 , 2 ]. Due to the advantages of the ergodicity, unpredictability, pseudo-randomness and initial value sensitivity [ 3 , 4 ], chaotic systems fit well to various chaos-based image encryptions [ 5 , 6 ] and secure communications [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Chen

et al. 2020

Entropy

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Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.

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“…Up to now, chaos is a very important research topic and received much attention in complicated nonlinear dynamics and chaotic cryptography [1]- [4]. As a model for convection between parallel plates, the Lorenz system with real variables is always a paradigm of chaos.…”

Section: Introductionmentioning

confidence: 99%

“…The coexistence of multi-attractors for the same group of parameters can be observed in a number of nonlinear circuits or systems [1], [21], [22], this phenomenon is called multistability. System displays different attractors depending on the different initial values.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a One-Parameter Chaotic System in Complex Field

Zhao

Liu

et al. 2020

IEEE Access

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Chaotic dynamics analysis of complex-variable chaotic systems (CVCSs) is an important problem in real secure communication and encryption. In this paper, a simple one-parameter chaotic system in complex field is proposed, whose nonlinear terms are the same as Lorenz system but the linear terms are much simpler. The proposed system has circular equilibria and therefore multi-stability can be measured by phase portraits, bifurcation diagrams and Lyapunov exponent spectrum. Its basin of attraction is filled with initial points leading to chaotic behaviors. The coexistence of infinitely many attractors is found in the proposed system, which is not reported in the existing complex-variable Lorenz system. Finally, two complexity indexes are used to measure dynamic characteristic with respect to parameter. INDEX TERMS Coexisting attractors, extreme multistability, complex-variable chaotic system, complexity.

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Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode

Cited by 146 publications

References 55 publications

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Dynamic Analysis of a One-Parameter Chaotic System in Complex Field

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