Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle |
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Authors: | Yanqin Wang Maoan Han |
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Affiliation: | 1. Applied Mathematics Department, Shanghai Normal University, Shanghai, 200234, PR China;2. School of Mathematics & Physics, Changzhou University, Changzhou, 213164, Jiangsu, PR China |
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Abstract: | In this paper, we deal with the problem of limit cycle bifurcation near a 2-polycycle or 3-polycycle for a class of integrable systems by using the first order Melnikov function. We first get the formal expansion of the Melnikov function corresponding to the heteroclinic loop and then give some computational formulas for the first coefficients of the expansion. Based on the coefficients, we obtain a lower bound for the maximal number of limit cycles near the polycycle. As an application of our main results, we consider quadratic integrable polynomial systems, obtaining at least two limit cycles. |
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Keywords: | Heteroclinic loop Near-integrable system Melnikov function Limit cycle bifurcation |
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