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November 2014
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12 Reads
Bifurcations in a cubic system with a degenerate saddle point are investigated using the technique of blow-up, the method of planar perturbation theory and qualitative analysis. It has been found that after appropriate perturbations, at least 12 limit cycles can bifurcate from a degenerate saddle point in a type of cubic systems.
September 2014
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11 Reads
Applied Mathematics and Computation
Asymptotic expansion formulae of the first order Melnikov function near the perturbed center of a cubic system are investigated studied through a suitable transformation. By expanding the formulae, we obtain that the given cubic system can have at least ten limit cycles.
