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On Behavior of the Periodic Orbits of a Hamiltonian System of Bifurcation of Limit Cycles

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  • Amor Menaceur
  • Mohamed Abdalla
  • Sahar Ahmed Idris
  • Ibrahim Mekawy

Abstract

In light of the previous recent studies by Jaume Llibre et al. that dealt with the finite cycles of generalized differential Kukles polynomial systems using the first- and second-order mean theorem such as (Nonlinear Anal., 74, 1261–1271, 2011) and (J. Dyn. Control Syst., vol. 21, 189–192, 2015), in this work, we provide upper bounds for the maximum number of limit cycles bifurcating from the periodic orbits of Hamiltonian system using the averaging theory of first order.

Suggested Citation

  • Amor Menaceur & Mohamed Abdalla & Sahar Ahmed Idris & Ibrahim Mekawy, 2021. "On Behavior of the Periodic Orbits of a Hamiltonian System of Bifurcation of Limit Cycles," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, September.
    • Handle: RePEc:hin:jnlmpe:1952706
    DOI: 10.1155/2021/1952706
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