Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis |
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Authors: | Yun Tian Pei Yu |
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Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, PR China;2. Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada |
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Abstract: | In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) 24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found. |
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Keywords: | 34C07 34C23 Bifurcation of limit cycles Higher-order analysis Darboux integral Focus value |
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