Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors

Cui, Li; Lu, Ming; Ou, Qingli; Duan, Hao; Luo, Wenhui

doi:10.1016/j.chaos.2020.109894

Cited by 58 publications

(29 citation statements)

References 49 publications

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“…Regarding fractional-order chaotic systems, we have published two articles on basin of attraction analysis [35,36]. In the present study, we further analyzed the characteristics of a basin of attraction and again analyzed the stability of the system by considering Lyapunov exponential function.…”

Section: Basin Of Attraction Analysismentioning

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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Section: Basin Of Attraction Analysismentioning

confidence: 99%

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

Ding

Cui

2021

Complexity

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“…It fully reflects the fact that the hidden chaotic attractor is a dialectical unity of local instability and multistability. In the next section of this paper, we will use the Lyapunov exponent to describe the basins of attraction of system (4) [23,24]. e analysis from Figure 4(b) shows how the positive Lyapunov exponent changes, which suggests that system (4) alternates between the quasiperiodic state and the chaotic state and fully depicts the changes in local instability and multistability of system (4).…”

Section: Analysis Of Bifurcation Lyapunov Exponent and Poincaré Sectionmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Cui

Chen

2021

Complexity

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A neural network is a model of the brain’s cognitive process, with a highly interconnected multiprocessor architecture. The neural network has incredible potential, in the view of these artificial neural networks inherently having good learning capabilities and the ability to learn different input features. Based on this, this paper proposes a new chaotic neuron model and a new chaotic neural network (CNN) model. It includes a linear matrix, a sine function, and a chaotic neural network composed of three chaotic neurons. One of the chaotic neurons is affected by the sine function. The network has rich chaotic dynamics and can produce multiscroll hidden chaotic attractors. This paper studied its dynamic behaviors, including bifurcation behavior, Lyapunov exponent, Poincaré surface of section, and basins of attraction. In the process of analyzing the bifurcation and the basins of attraction, it was found that the network demonstrated hidden bifurcation phenomena, and the relevant properties of the basins of attraction were obtained. Thereafter, a chaotic neural network was implemented by using FPGA, and the experiment proved that the theoretical analysis results and FPGA implementation were consistent with each other. Finally, an energy function was constructed to optimize the calculation based on the CNN in order to provide a new approach to solve the TSP problem.

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“…An analog/digital or mixed circuit realization of the proposed transformed fractional-order chaotic systems can be presented in future work based on (10) or simplified forms of it. This can be performed by combining similar previous designs of GL-based fractional-order systems [72] and rotated chaotic systems [47] realizations.…”

Section: ) Multiple Wings Distributed On a Predefined Or Arbitrary Line Curve Or Surfacementioning

confidence: 99%

“…Circuit realization of chaotic systems is a requirement in many applications [7], [8], [9]. Circuit implementation of fractional-order multi-wing hidden attractors is a flourishing research topic [10]. Hence, circuit requirements should be taken into consideration when proposing new, modified or generalized chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Self-Reproducing Hidden Attractors in Fractional-Order Chaotic Systems Using Affine Transformations

Sayed

Radwan

2020

IEEE Open J. Circuits Syst.

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This article proposes a unified approach for hidden attractors control in fractional-order chaotic systems. Hidden attractors have small basins of attractions and are very sensitive to initial conditions and parameters. That is, they can be easily drifted from chaotic behavior into another type of dynamics, which is not suitable for encryption applications that require quite wide initial conditions and parameters ranges for encryption key design. Hence, a systematic coordinate affine transformation framework is utilized to construct transformed systems with self-reproducing attractors. Simulation results of two three-dimensional fractional-order chaotic systems with hidden attractors validate that the proposed framework supports attractors geometric structure design and multi-wing generation. Hidden attractor size, polarity, phase, shape and position control while preserving the chaotic dynamics is indicated by strange attractors, spectral entropy, maximum Lyapunov exponent and bifurcation diagrams. Simulations demonstrate the capability of multi-wing generation from fractional-order hidden attractors with no equilibria using non-autonomous parameters as opposed to the classical equilibria extension techniques suitable only for self-excited attractors. The self-reproduced multiple wings can share the same center point or be distributed along an arbitrary line, curve or surface thanks to the non-autonomous translation parameters. Multi-wing attractors widen the basin of attraction and enlarge the state space volume. For practical applications, the proposed technique makes fractional-order systems with hidden attractors suitable for circuit implementations that require specific signal level and polarity conditions. In addition, for digital encryption applications, the relatively wide range of the extra parameters enhances the key space and hence the robustness against brute force attacks.

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Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors

Cited by 58 publications

References 49 publications

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

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

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Self-Reproducing Hidden Attractors in Fractional-Order Chaotic Systems Using Affine Transformations

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