Abstract
In this paper, we investigate the number, location and stability of limit cycles in a class of perturbed polynomial systems with (2n + 1) or (2n + 2)-degree by constructing detection function and using qualitative analysis. We show that there are at most n limit cycles in the perturbed polynomial system, which is similar to the result of Perko in [8] by using Melnikov method. For n = 2, we establish the general conditions depending on polynomial’s coefficients for the bifurcation, location and stability of limit cycles. The bifurcation parameter value of limit cycles in [5] is also improved by us. When n = 3 the sufficient and necessary conditions for the appearance of 3 limit cycles are given. Two numerical examples for the location and stability of limit cycles are used to demonstrate our theoretical results.
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1 Supported by Natural Science Foundation of China (10261008) and "Creative Project" (KZCZ2-SW-118) in Chinese Academy of Sciences.
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Yang1, Cx., Wang, Rq. Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems. Acta Mathematicae Applicatae Sinica, English Series 20, 155–166 (2004). https://doi.org/10.1007/s10255-004-0158-y
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DOI: https://doi.org/10.1007/s10255-004-0158-y