Analysis of a Shil’nikov Type Homoclinic Bifurcation
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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.
KeywordsHomoclinic bifurcation Hopf bifurcation Poincaré map
MR(2010) Subject Classification34C23 34C37 37C29
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The authors would like to thank the referees for their helpful comments and suggestions.
- Belykov, L. A.: Bifurcation of system with homoclinic curve of a saddle-focus with saddle quantity zero. Math. Z., 36, 838–843 (1984)Google Scholar
- Shilnikov, L. P.: A case of the existence of a countable number of periodic motions. Sov. Math. Dokl., 6, 163–166 (1965)Google Scholar