An infinite 2-D lattice of strange attractors

Li, Chunbiao; Sprott, Julien Clinton; Mei, Yong

doi:10.1007/s11071-017-3612-0

Cited by 100 publications

(30 citation statements)

References 53 publications

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“…Multistable systems have multiple solutions under different initial conditions, and the self-reproducing system is a new kind of multistable system with infinitely many coexisting attractors by reproducing themselves along particular dimensions or directions. It should be pointed out that all of those coexisting attractors in a system share the same Lyapunov exponents, and the infinitely many attractors in self-reproducing chaotic systems are triggered by the initial condition [11,12]. Therefore, it is interesting to check whether those coexisting attractors have the same complexity.…”

Section: Complexity Analysis Of Self-reproducing Chaotic Systemsmentioning

confidence: 99%

“…Multistability in circuit implementation [6], synchronization [7], image encryption [8] and neural networks [9] have also aroused much interest. Multistable systems can have a limited number of coexisting attractors [10] or even infinitely many attractors [11,12]. Specifically, Li et al proposed a class of self-reproducing systems (one case of conditional symmetry) giving one-dimensional infinitely many attractors [11] and a unique case with a two-dimensional lattice of infinitely many strange attractors by introducing periodic trigonometric functions into a two-dimensional offset-boostablesystem [12].…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

Sun

et al. 2018

Entropy

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Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.

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Section: Complexity Analysis Of Self-reproducing Chaotic Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

Sun

et al. 2018

Entropy

Self Cite

View full text Add to dashboard Cite

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“…It has inherent properties of ergodicity, sensitivity of initial value and parameters, and complex dynamic characteristic [4,5]. Especially, chaotic attractors coexist [6,7]. Therefore, a chaos system could be used in the image encryption fields.…”

Section: Introductionmentioning

confidence: 99%

Fractional-order 4D hyperchaotic memristive system and application in color image encryption

Mou

et al. 2019

J Image Video Proc.

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In this paper, some properties of the fractional-order four-dimensional (4D) hyperchaotic memristive system are analyzed by the phase diagram, Lyapunov exponent spectrum and bifurcation diagram according to the Adomian decomposition method. Based on the chaotic system, a color image encryption scheme is proposed through combining the DNA sequence operation. The algorithm simulation results and security feature analysis show that the encryption scheme has good encryption effect and high safety performance, which provides an experimental basis and theoretical guidance for the safe transmission of image information.

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“…Particularly, memristive systems based on ideal memristors can produce the extreme multistability phenomenon of coexisting infinitely many attractors [22,23]. Such a special phenomenon is commonly triggered in the systems with no equilibrium [24] or infinitely many equilibria [16,[25][26][27][28], entirely different from those generated from the offset-boostable flow by introducing an extra periodic 2 Complexity signal [29][30][31]. In [17], a memristor-based Colpitts chaotic oscillator was proposed by introducing a nonideal extended memristor into original Colpitts oscillator [2].…”

Section: Introductionmentioning

confidence: 99%

Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor‐Based Colpitts System

et al. 2019

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In this paper, a four-dimensional (4-D) memristor-based Colpitts system is reaped by employing an ideal memristor to substitute the exponential nonlinear term of original three-dimensional (3-D) Colpitts oscillator model, from which the initials-dependent extreme multistability is exhibited by phase portraits and local basins of attraction. To explore dynamical mechanism, an equivalent 3-D dimensionality reduction model is built using the state variable mapping (SVM) method, which allows the implicit initials of the 4-D memristor-based Colpitts system to be changed into the corresponding explicitly initials-related system parameters of the 3-D dimensionality reduction model. The initials-related equilibria of the 3-D dimensionality reduction model are derived and their initials-related stabilities are discussed, upon which the dynamical mechanism is quantitatively explored. Furthermore, the initials-dependent extreme multistability is depicted by two-parameter plots and the coexistence of infinitely many attractors is demonstrated by phase portraits, which is confirmed by PSIM circuit simulations based on a physical circuit.

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An infinite 2-D lattice of strange attractors

Cited by 100 publications

References 53 publications

Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

Fractional-order 4D hyperchaotic memristive system and application in color image encryption

Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor‐Based Colpitts System

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