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Keywords = asymptotic expansion (AE)

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12 pages, 409 KiB  
Article
Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop
by Erli Zhang and Stanford Shateyi
Mathematics 2023, 11(18), 3944; https://doi.org/10.3390/math11183944 - 17 Sep 2023
Cited by 1 | Viewed by 1167
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Application of Mathematical Method and Models in Dynamic System)
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