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Limit Cycles Of A Class Of Perturbed Differential Systems Bifurcating From An Unperturbed Hamiltonian Center

Author

Listed:
  • AMOR MENACEUR

    (Laboratory of ACED, Department of Mathematics, University of Guelma, P. O. Box 401, Guelma 24000, Algeria)

  • YASSINE BOUATTIA

    (Advanced Control laboratory (LABCAV), Department of Mathematics University of Guelma, P. O. Box 401 Guelma 24000, Algeria)

  • SALEM ALKHALAF

    (Department of Computer Engineering College of Computer, Qassim University Buraydah, Saudi Arabia)

  • ASMA ALHARBI

    (Department of Mathematics College of Science, Qassim University Buraydah 51452, Saudi Arabia)

Abstract

We study the number of limit cycles of the following planar differential system: u̇ = v2a−1 − 𠜀(1 + Sn2m1ϕ)G1(u,v),v̇ = −v2b−1 − 𠜀(1 + Cs2m2ϕ)G2(u,v), where a,b,m1,m2 are positive integers, for every h = 1, 2, the polynomial Gh(u,v) has degree nh ≥ 2 with Gh(0, 0) = 0, Cs(ϕ) and Sn(ϕ) are generalized trigonometric functions and 𠜀 is a small parameter. We provide an accurate upper bound of the maximum number of limit cycles such that the above system can have bifurcation from an unperturbed Hamiltonian center, using the averaging theory of the first order. These findings contribute to the broader understanding of nonlinear dynamics and have potential applications in various fields such as control systems, signal processing, and artificial intelligence.

Suggested Citation

  • Amor Menaceur & Yassine Bouattia & Salem Alkhalaf & Asma Alharbi, 2025. "Limit Cycles Of A Class Of Perturbed Differential Systems Bifurcating From An Unperturbed Hamiltonian Center," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(08), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:08:n:s0218348x25401450
    DOI: 10.1142/S0218348X25401450
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