Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis

Zhang, Yunzhen; Liu, Zhong; Wu, Huagan; Chen, Shengyao; Bao, Bocheng

doi:10.1016/j.chaos.2019.07.004

Cited by 70 publications

(34 citation statements)

References 37 publications

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“…In many applications, the chaotic behavior is undesirable because of the fact that even small disturbances may cause the states to diverge exponentially. Therefore, the chaos phenomenon should be avoided or completely suppressed in practice [6][7][8][9]. In the past two decades, chaos synchronization has generated important interests in applied fields such as secure communication [10,11], electronic circuits [12], optical chaotic communication [13], chaotic CO2 lasers [14], chaotic finance system [15], a periodically intermittent control [16], partial discharge in power cables [17], cryptosystems [18] and image encryption [19].…”

Section: Introductionmentioning

confidence: 99%

A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security

et al. 2021

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This paper proposes a disturbance observer-based Sliding Mode Control (SMC) approach for the robust synchronization of uncertain delayed chaotic systems. This is done by, first, examining and analyzing the electronic behavior of the master and slave Sprott chaotic systems. Then, synthesizing a robust sliding mode control technique using a newly proposed sliding surface that encompasses the synchronization error between the master and slave. The external disturbances affecting the system were estimated using a disturbance observer. The proof of the semi-globally bounded synchronization between the master and slave was established using the Lyapunov stability theory. The efficiency of the proposed approach was first assessed using a simulation study, then, experimentally validated on a data security system. The obtained results confirmed the robust synchronization properties of the proposed approach in the presence of timedelays and external disturbances. The experimental validation also confirmed its ability to ensure the secure transfer of data. INDEX TERMS Sliding mode control; robust synchronization control; chaotic systems; disturbance observer; data security.

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Section: Introductionmentioning

confidence: 99%

A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security

et al. 2021

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“…At present, the generation and application of multistability and extreme multistability has become a very hot topic for chaotic circuit systems [25][26][27][28][29]. Compared with other chaotic systems, combining memristors with chaotic systems can generate chaotic attractors possessing complicated dynamic properties.…”

Section: Introductionmentioning

confidence: 99%

Basin of Attraction Analysis of New Memristor‐Based Fractional‐Order Chaotic System

Ding

Cui

2021

Complexity

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Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

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“…Recently there has been growing attention in finding chaotic systems with special qualities. Systems with no equilibrium [3], [4], with stable equilibria [5], [6], with curves of equilibria [7][8][9], with surface of equilibria [10][11][12], with multi-scroll attractors [13], with hidden attractors [14], [15], with amplitude control [16], [17], with simplest form , having hyperchaos [18][19][20], having fractional order form [21][22][23], with topological horseshoes [24], [25], and with extreme multistability [26][27][28][29], are examples of them. Another major category of chaotic systems includes periodically-forced nonlinear oscillators [30].…”

Section: Introductionmentioning

confidence: 99%

A Novel Mega-stable Chaotic Circuit

Pham¹,

Ali²,

Al-Saidi³

et al. 2020

RADIOENGINEERING

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In recent years designing new multistable chaotic oscillators has been of noticeable interest. A multistable system is a double-edged sword which can have many benefits in some applications while in some other situations they can be even dangerous. In this paper, we introduce a new multistable two-dimensional oscillator. The forced version of this new oscillator can exhibit chaotic solutions which makes it much more exciting. Also, another scarce feature of this system is the complex basins of attraction for the infinite coexisting attractors. Some initial conditions can escape the whirlpools of nearby attractors and settle down in faraway destinations. The dynamical properties of this new system are investigated by the help of equilibria analysis, bifurcation diagram, Lyapunov exponents' spectrum, and the plot of basins of attraction. The feasibility of the proposed system is also verified through circuit implementation.

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Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis

Cited by 70 publications

References 37 publications

A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security

A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security

Basin of Attraction Analysis of New Memristor‐Based Fractional‐Order Chaotic System

A Novel Mega-stable Chaotic Circuit

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