Segmented disc dynamo with symmetric multidirectional patterns of multiscroll chaotic attractors

Azam, Anam; Aqeel, Muhammad; Sunny, Danish Ali

doi:10.1016/j.matcom.2022.04.005

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…Recently, the authors of [8] studied the complex dynamics of the equilibrium point of system (2) by using the center manifold theory, and determined the existence conditions of Hopf bifurcation, at the same time, the Darboux integrability of the system was discussed in detail. For the mechanism of chaos in system (2), some theoretical and numerical analyses were also given in [9] and [10] successively.…”

Section: Introductionmentioning

confidence: 99%

Multiple limit cycles bifurcation and Jacobi stability for a class of segmented disc dynamo system

Liu,

Wang,

Huang

2024

Preprint

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In this paper, the multiple bifurcation of limit cycles for a segmented disc dynamo system is studied. The formal series method for calculating the singular point quantities is applied to determine the highest order focus value at Hopf bifurcation point. For two cases of the segmented disc dynamo system, namely the system with or without friction coefficient (abbr. SDDF- or SDD-model), the maximum number of limit cycles is obtained at the symmetrical equilibrium points under the condition of synchronous perturbation respectively. At the same time, the parameters condition is classified for exact number of limit cycles near each weak focus. Finally, we find that all equilibrium points of the heart model are Jacobi unstable under certain parameter values.

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Section: Introductionmentioning

confidence: 99%

Multiple limit cycles bifurcation and Jacobi stability for a class of segmented disc dynamo system

Liu,

Wang,

Huang

2024

Preprint

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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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Segmented disc dynamo with symmetric multidirectional patterns of multiscroll chaotic attractors

Cited by 2 publications

References 31 publications

Multiple limit cycles bifurcation and Jacobi stability for a class of segmented disc dynamo system

Multiple limit cycles bifurcation and Jacobi stability for a class of segmented disc dynamo system

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

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