Homoclinic flip bifurcations accompanied by transcritical bifurcation

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.

Keywords

Transcritical bifurcation / Homoclinic orbit / Periodic orbit / Local coordinate system / Poincaré maps

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