Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (3): 1169-1187.doi: 10.1007/s10473-025-0322-4

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HOPF BIFURCATION PROBLEM BY PERTURBING A CLASS OF QUARTIC LINEAR-LIKE HAMILTONIAN SYSTEMS

Yanqin XIONG, Guangping HU   

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • Received:2023-02-23 Revised:2024-01-01 Online:2025-05-25 Published:2025-09-30
  • Contact: Yanqin XIONG, E-mail: yqxiong@nuist.edu.cn
  • About author:Guangping HU, E-mail: hugp@nuist.edu.cn
  • Supported by:
    National Natural Science Foundations of China (12371171) and the Natural Science Foundation of Jiangsu Province (BK20221339).

Abstract: We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.

Key words: quartic near-Hamiltonian system, phase portrait, Hopf bifurcation, Hopf cyclicity

CLC Number: 

  • 34C05
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