Abstract
The bifurcation associated with a homoclinic orbit to saddle-focus including a pair of pure imaginary eigenvalues is investigated by using related homoclinic bifurcation theory. It is proved that, in a neighborhood of the homoclinic bifurcation value, there are countably infinite saddle-node bifurcation values, period-doubling bifurcation values and double-pulse homoclinic bifurcation values. Also, accompanied by the Hopf bifurcation, the existence of certain homoclinic connections to the periodic orbit is proved.
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Supported by National NSF (Grant Nos. 11371140, 11671114) and Shanghai Key Laboratory of PMMP
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Xu, Y.C., Liu, X.B. Analysis of a Shil’nikov Type Homoclinic Bifurcation. Acta. Math. Sin.-English Ser. 34, 901–910 (2018). https://doi.org/10.1007/s10114-018-5236-9
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DOI: https://doi.org/10.1007/s10114-018-5236-9