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Homoclinic flip bifurcations accompanied by transcritical bifurcation

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Abstract

The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Xingbo Liu

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  1. Xingbo Liu
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Correspondence to Xingbo Liu.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10801051) and the Shanghai Leading Academic Discipline Project (No.B407).

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Liu, X. Homoclinic flip bifurcations accompanied by transcritical bifurcation. Chin. Ann. Math. Ser. B 32, 905–916 (2011). https://doi.org/10.1007/s11401-011-0675-y

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  • DOI: https://doi.org/10.1007/s11401-011-0675-y

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