Forthcoming and Online First Articles

International Journal of Dynamical Systems and Differential Equations

International Journal of Dynamical Systems and Differential Equations (IJDSDE)

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International Journal of Dynamical Systems and Differential Equations (1 paper in press)

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  • Third-Order Bifurcation of Limit Cycles for a Perturbed Quartic Isochronous Center   Order a copy of this article
    by Bo Huang, Linping Peng 
    Abstract: In this article, we study how many limit cycles can bifurcate from the periodic orbits of a quartic uniform isochronous centre when it is perturbed inside a class of quartic polynomial differential systems. Using the first and second order averaging method, we provide the maximum number of limit cycles, 3 and 5 respectively, that can bifurcate from the periodic orbits around the centre. Using the third order averaging method, we show that at least five limit cycles can bifurcate from the periodic orbits around the centre. Our main theorem has improved and generalised some known results in published papers.
    Keywords: averaging method; limit cycles; period annulus; polynomial perturbation; quartic centre.
    DOI: 10.1504/IJDSDE.2023.10056612