Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization

Ma, Chenguang; Mou, Jun; Li, Xiong; Banerjee, Santo; Liu, Tianming; Han, Xintong

doi:10.1007/s11071-021-06276-8

Cited by 112 publications

(42 citation statements)

References 49 publications

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“…Zolfaghari-Nejad et al confirmed the period-subtracting phenomenon through SE distribution diagram [31]. Wang et al analyzed the basic dynamics of a fractional-order chaotic system with a hidden system by comparing LLE and SE algorithms in [32], and the SE algorithm was also used to exhibit multi-stability under different initial values [33][34][35]. In this paper, we give the specific normalized average values, based on which the state of the studied chaotic system can be identified.…”

Section: Introductionmentioning

confidence: 97%

A Hidden Chaotic System with Multiple Attractors

Zhang

Tian

et al. 2021

Entropy

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This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

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Section: Introductionmentioning

confidence: 97%

A Hidden Chaotic System with Multiple Attractors

Zhang

Tian

et al. 2021

Entropy

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“…Any chaotic signal has its inherent features namely identified as scale (C. Sprott and Xiong 2015;C. Sprott 2010;Gu et al 2021;Lu et al 2019;Liu et al 2020;Wang et al 2020;Zhao et al 2020;Akgul et al 2016Akgul et al , 2019Falco et al 2012) and offset (Li et al 2019(Li et al , 2017aLiu et al 2020;Li and Sprott 2017;Li et al 2021Li et al , 2017bKingni et al 2020;Ma et al 2021;Zhang et al 2018;Mezatio et al 2019;Bao et al 2020;Chen et al 2020;Zhang et al 2020;Wu et al 2019a;Ding et al 2020). For rescaling a chaotic signal, people usually design dynamical systems with amplitude control from the very beginning.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason, offset boosting has attracted great interests recently both in continuous system and in discrete maps. Researchers pays great effort to learn how to get those attractors controlled by parameters (Li et al 2017b;Kingni et al 2020;Ma et al 2021;Zhang et al 2018;Mezatio et al 2019) or by initial conditions (Bao et al 2020;Chen et al 2020;Zhang et al 2020;Wu et al 2019a;Ding et al 2020). Even in those memristive systems (Chen et al 2019;Kengne et al 2018;Lu et al 2020;Wu et al 2019b;Yuan et al 2019) offset boosting is still a hot spot for discussion.…”

Section: Introductionmentioning

confidence: 99%

On Offset Boosting in Chaotic System

Jiang

2021

Chaos Theory and Applications

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Offset boosting is an important issue for chaos control due to its broadband property and polarity control. There are two main approaches to realize offset boosting. One is resort to parameter introducing where an offset booster realizes attractor boosting. The other one is by the means of periodic function or absolute value function where any self-reproduced or doubled attractors with diverse offset are extracted out by a specific initial condition. The former also provides a unique window for observing multistability and the latter gives the direction for constructing desired multistability.

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“…Ye et al [25] analyzed the complexity characteristics of Bao chaotic system, Rossler chaotic system and Wien Bridge hyperchaotic system based on SE and C0 algorithms. Ma et al [26] used chaos graph based on SE complexity to realize the simultaneous change of bifurcation parameters and analyzed the difference of complexity of the system under different initial values. Li et al [27] showed that SE and C0 complexity algorithms had higher computational accuracy and had more obvious basis for parameter selection of chaos map.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Complexity of the Switchable Chaotic Systems and its FPGA Implementation

Yan

Qiyu

2021

Preprint

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A four-dimensional chaotic system with complex dynamical properties is constructed via introducing a nonlinear function term. The paper assesses complexity of the system employing equilibrium points, Lyapunov exponent spectrum and bifurcation model. Specially, the coexisting Lyapunov exponent spectrum and the coexisting bifurcation validate the coexistence of attractors. The corresponding complexity characteristics of the system can be analyzed by using C0 and spectral entropy(SE) complexity algorithms, and the most complicated integer-order system is obtained. Furthermore, the circuit which can switch the chaotic attractors is implemented. It is worth noting that the more sophisticated parameters are received by comparing the complexity of the most complicated integer-order chaotic system with corresponding fractional-order chaotic system. Finally, the results of simulation model built in the MATLAB are the same as the hardware verified on the Field-Programmable Gate Array(FPGA) platform, which verify the feasibility of the system.

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Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization

Cited by 112 publications

References 49 publications

A Hidden Chaotic System with Multiple Attractors

A Hidden Chaotic System with Multiple Attractors

On Offset Boosting in Chaotic System

Comparison of Complexity of the Switchable Chaotic Systems and its FPGA Implementation

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