Bifurcation of Limit Cycles of a Piecewise Smooth Hamiltonian System

Yang, Jihua; Zhao, Liang

doi:10.1007/s12346-022-00674-y

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…Deriving a mathematical representation for the Melnikov mapping whose order is 1 has a key function in the examination of LC bifurcations. This topic has been renewed very recently in some works such as [29,30]. Employing the theory called averaging based on the first order, the authors of [31] investigated LC bifurcations by using the steady isochronous epicenter whose orbits are periodical regarding…”

Section: Background and Literaturementioning

confidence: 99%

Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

Zhang,

Yang,

Shateyi

2023

Mathematics

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Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions are dealt with. A Melnikov mapping whose order is one is implicitly obtained by finding its originators when the system is perturbed under any nth degree of real polynomials. Then, the approach employing the Picard–Fuchs mapping is utilized to attain a higher boundary of bifurcation LCNs of systems composed of PSD functions with a global center. The method we used could be implemented to examine the problems related to the LC of other PSDS.

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Section: Background and Literaturementioning

confidence: 99%

Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

Zhang,

Yang,

Shateyi

2023

Mathematics

Self Cite

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“…Additionally, this theory bears relevance to Hilbert's 16th problem, adding further significance to its exploration. As a result, the investigation of LC bifurcation within differential systems (piecewise smooth) has emerged as a prominent and dynamic area of research in recent years [3][4][5].…”

Section: Introductory Notesmentioning

confidence: 99%

Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop

Zhang,

Shateyi

2023

Mathematics

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This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m. By analyzing the asymptotic expansion (AE) of the Melnikov function with first-order M(h) near the generalized heteroclinic loop (HL), we utilize the expansions of the corresponding generators. This approach allows us to establish both lower and upper bounds for the quantity of limit cycles in the perturbed system. Our analysis involves a combination of expansion techniques, derivations, and divisions to derive these findings.

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The limit cycle bifurcations of a whirling pendulum with piecewise smooth perturbations

Yang

2024

Acta Math Sci

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Bifurcation of Limit Cycles of a Piecewise Smooth Hamiltonian System

Cited by 4 publications

References 23 publications

Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop

The limit cycle bifurcations of a whirling pendulum with piecewise smooth perturbations

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