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ON THIRD-ORDER NILPOTENT CRITICAL POINTS: INTEGRAL FACTOR METHOD
https://doi.org/10.1142/S0218127411029161Cited by:23
Abstract
For third-order nilpotent critical points of a planar dynamical system, the problem of characterizing its center and focus is completely solved in this article by using the integral factor method. The associated quasi-Lyapunov constants are defined and their computation method is given. For a class of cubic systems under small perturbations, it is proved that there exist eight small-amplitude limit cycles created from a nilpotent critical point.
This research was partially supported by the National Natural Science Foundation of China (10831003 and 11071222).
Keywords:
References
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