Stochastic generation and shifts of phantom attractors in the 2D Rulkov model

Bashkirtseva, Irina; Ryashko, Lev

doi:10.1016/j.chaos.2022.112111

Cited by 10 publications

(1 citation statement)

References 37 publications

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“…As well known, the chaotic attractors of dynamical systems can be classified as self-excited and hidden, which may contain one-scroll, two-scrolls, multiwing, and multi-scrolls. In literature, the scientific community has been working hard to propose novel chaotic systems in discrete (maps) or continuous (flows) domains since they could mean a step forward in understanding physical phenomena with significant engineering applications [1][2][3][4][5][6][7][8]. However, there is still a need for new chaotic systems encompassing recent approaches, like quantum chaos, hidden attractors, multi-stability, and fractional-order calculus, among others.…”

Section: Introductionmentioning

confidence: 99%

Fractional-order projection of a chaotic system with hidden attractors and its passivity-based synchronization

Serrano,

Munoz-Pacheco,

Flores

2023

Front. Appl. Math. Stat.

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This paper presents the fractional-order projection of a chaotic system, which delivers a collection of self-excited and hidden chaotic attractors as a function of a single system parameter. Based on an integer-order chaotic system and the proposed transformation, the fractional-order chaotic system obtains when the divergence of integer and fractional vector fields flows in the same direction. Phase portraits, bifurcation diagrams, and Lyapunov exponents validate the chaos generation. Apart from these results, two passivity-based fractional control laws are designed effectively for the integer and fractional-order chaotic systems. In both cases, the synchronization schemes depend on suitable storage functions given by the fractional Lyapunov theory. Several numerical experiments confirm the proposed approach and agree well with the mathematical deductions.

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