A New 4D Chaotic System with Two‐Wing, Four‐Wing, and Coexisting Attractors and Its Circuit Simulation

Huang, Ling; Zhang, Zefeng; Xiang, Jianhong; Wang, Shiming

doi:10.1155/2019/5803506

Cited by 17 publications

(12 citation statements)

References 29 publications

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“…It was mentioned that this system "can generate chaotic butterfly attractors of two wings and four wings at the same time" [28] depending on the dimensions visualized, as seen in the paper and in Figure 10. In the figure from the paper, X-Y, X-Z, Y-Z, and Z-W plots clearly show two wings of an attractor.…”

Section: E Four-dimensional Chaotic System Resultsmentioning

confidence: 97%

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Analysis and Visualization of High‐Dimensional Dynamical Systems’ Phase Space Using a Network‐Based Approach

Luce

Sayama

2022

Complexity

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The concept of attractors is considered critical in the study of dynamical systems as they represent the set of states that a system gravitates toward. However, it is generally difficult to analyze attractors in complex systems due to multiple reasons including chaos, high-dimensionality, and stochasticity. This paper explores a novel approach to analyzing attractors in complex systems by utilizing networks to represent phase spaces. We accomplish this by discretizing phase space and defining node associations with attractors by finding sink strongly connected components (SSCCs) within these networks. Moreover, the network representation of phase space facilitates the use of well-established techniques of network analysis to study the phase space of a complex system. We show the latter by introducing a new node-based metric called attractivity which can be used in conjunction with the SSCC as they are highly correlated. We demonstrate the proposed method by applying it to several chaotic dynamical systems and a large-scale agent-based social simulation model.

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Section: E Four-dimensional Chaotic System Resultsmentioning

confidence: 97%

“…Lastly, we will test our method against a system with more than three dimensions. Equation (5) is the system of differential equations found in [28] containing different kinds of attractors. However with our results, we argue that the different kinds of attractors are all part of one multidimensional attractor.…”

Section: Four-dimensional Chaoticmentioning

confidence: 99%

Analysis and Visualization of High‐Dimensional Dynamical Systems’ Phase Space Using a Network‐Based Approach

Luce

Sayama

2022

Complexity

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“…According to their dimensions, existing chaotic systems can be divided into low-dimensional chaotic systems and high-dimensional chaotic systems [9][10][11][12][13][14][15]. The author of [9] presented a four-dimensional quadratic autonomous hyperchaotic system based on the Lorenz system, which has only one hyperchaotic attractor.…”

Section: Introductionmentioning

confidence: 99%

“…The authors of [11] presented a new four-dimensional hyperchaotic system with coexisting attractors, which has several dynamic behaviours and utilizes a hyperchaotic system constructor state-error controller. The authors of [12] presented a new fourdimensional chaotic system with multi-wing and coexisting attractors and simulated its circuit. The authors of [13] presented a new four-dimensional hyperchaotic system and applied it to image encryption.…”

Section: Introductionmentioning

confidence: 99%

A Novel Chaotic Block Image Encryption Algorithm Based on Deep Convolutional Generative Adversarial Networks

Fang

Liu

2021

IEEE Access

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This paper proposes a novel chaotic block image encryption algorithm based on deep convolutional generative adversarial networks (DCGANs), quaternions, an improved Feistel network, and an overall scrambling and diffusion mechanism. First, a new hyperchaotic system is introduced and combined with DCGANs to generate a random sequence with better randomness and complexity as a key stream. This sequence is then combined with a quaternion and an improved Feistel network encryption of a colour plaintext image by utilizing the key block matrix to ultimately achieve overall scrambling and diffusion of the cipher image. Finally, the security of this algorithm is quantitatively and qualitatively analysed. The simulation results show that the proposed hyperchaotic system has a large key space and good random characteristics and that the new algorithm yields adequate security and can resist brute-force attacks and chosen-plaintext attacks. Therefore, this approach provides a new way to achieve secure transmission and protection of image information. INDEX TERMS Image encryption, chaotic system, deep convolutional generative adversarial networks.

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“…e discovery of memristors has caused an upsurge in studying and applying memristors. Due to the nonlinearity of memristor, it has been applied in many fields, such as flash memory [2,3], neuromorphic computing [4,5], neural network [6,7], and chaotic system [8][9][10][11] based on chaos synchronization for encryption algorithms [12,13] and secure communication [14,15].…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

et al. 2020

Self Cite

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In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.

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A New 4D Chaotic System with Two‐Wing, Four‐Wing, and Coexisting Attractors and Its Circuit Simulation

Cited by 17 publications

References 29 publications

Analysis and Visualization of High‐Dimensional Dynamical Systems’ Phase Space Using a Network‐Based Approach

Analysis and Visualization of High‐Dimensional Dynamical Systems’ Phase Space Using a Network‐Based Approach

A Novel Chaotic Block Image Encryption Algorithm Based on Deep Convolutional Generative Adversarial Networks

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

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