Self-excited and hidden attractors in a novel chaotic system with complicated multistability

Natiq, Hayder; Said, Mohamad Rushdan Md.; Ariffin, Muhammad Rezal Kamel; He, Shaobo; Rondoni, Lamberto

doi:10.1140/epjp/i2018-12360-y

Cited by 61 publications

(27 citation statements)

References 31 publications

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“…The fractional-order chaotic system we proposed has higher complexity, and its polarity, amplitude, and frequency are freely adjustable, which is more valuable in practical engineering applications [23]- [26]. Nowadays, more and more researchers are concerned that the multistability phenomena in the chaotic dynamic behavior [27]- [36]. For example, Bao et al established a new five-dimensional dynamic system based on the memristive chaotic circuit, and its extreme multiple stability is analyzed in Ref [37].…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

Liu

Yan

et al. 2020

IEEE Access

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In this paper, the fractional calculus is introduced into a simplest memristive circuit to construct a new four-dimensional fractional-order chaotic system. Combining conformable differential definition and Adomian decomposition method (ADM) algorithm is used to solve the numerical solution of the system. The attractor coexistence of the fractional-order system is investigated from the attractor phase diagram, coexistence bifurcation model, coexistence Lyapunov exponent spectrum and attractor basin. In addition, the hardware circuit of the system is implemented on the DSP platform. The simulation results show that the fractional-order chaotic system exhibits rich dynamic characteristics. In particular, the initial value of the system could control the offset, amplitude and frequency of the attractor better, and increase the complexity and randomness of the chaotic sequences. The research provides theoretical basis and guidance for the applications of fractional-order chaotic system.

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Section: Introductionmentioning

confidence: 99%

A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

Liu

Yan

et al. 2020

IEEE Access

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“…Some nonlinear systems can exhibit many solutions with specified parameters and distinct initial conditions [10]. is nonlinear behavior is termed as coexisting attractors or multistability.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Prasad

Mukherjee²,

Saha

et al. 2020

Complexity

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Dynamical complexity and multistability of electrostatic waves are investigated in a four-component homogeneous and magnetized lunar wake plasma constituting of beam electrons, heavier ions (alpha particles, He ++ ), protons, and suprathermal electrons. e unperturbed dynamical system of the considered lunar wake plasma supports nonlinear and supernonlinear trajectories which correspond to nonlinear and supernonlinear electrostatic waves. On the contrary, the perturbed dynamical system of lunar wake plasma shows different types of coexisting attractors including periodic, quasiperiodic, and chaotic, investigated by phase plots and Lyapunov exponents. To confirm chaotic and nonchaotic dynamics in the perturbed lunar wake plasma, 0 − 1 chaos test is performed. Furthermore, a weighted recurrence-based entropy is implemented to investigate the dynamical complexity of the system. Numerical results show existence of chaos with variation of complexity in the perturbed dynamics.

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“…Li et al [12] introduced a new method for constructing self-reproducing chaotic systems with extreme multistability behaviors, in which the coexisting attractors reside in the phase space along a specific coordinate axis. Natiq et al [13] presented a simple chaotic system with trigonometric function term generating extreme multistability behaviors. Wang et al [14] proposed a four-wing memristive chaotic system with various multistability behaviors.…”

Section: Introductionmentioning

confidence: 99%

Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers

Natiq

Banerjee

Misra

2019

Chaos, Solitons & Fractals

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In this work, the dynamical behaviors of a low-dimensional model, which governs the interplay between a driver associated with pressure gradient and relaxation of instability due to magnetic field perturbations, are investigated. Besides that, two nonlinear controllers are constructed precisely to shift the equilibria of the plasma model apart from each other. Simulation results show that shifting the equilibria can change the spacing of chaotic attractors, and subsequently break the butterfly wings into one or two symmetric pair of coexisting chaotic attractors. Furthermore, stretching the equilibria of the system apart enough from each other gives rise to degenerate the butterfly wings into several periodic orbits. In addition, with appropriate initial conditions, the complex multistability behaviors including the coexistence of butterfly chaotic attractor with two point attractors, the coexistence of transient transition chaos with completely quasi-periodic behavior, and the coexistence of symmetric Hopf bifurcations are also observed.

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Self-excited and hidden attractors in a novel chaotic system with complicated multistability

Cited by 61 publications

References 31 publications

A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers

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