Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria

Abstract EN

The bifurcations ofheteroclinic loop with one nonhyperbolic equilibrium and onehyperbolic saddle are considered, where the nonhyperbolicequilibrium is supposed to undergo a transcritical bifurcation;moreover, the heteroclinic loop has an orbit flip and an inclinationflip.

When the nonhyperbolic equilibrium does not undergo atranscritical bifurcation, we establish the coexistence andnoncoexistence of the periodic orbits and homoclinic orbits.

While the nonhyperbolic equilibrium undergoes the transcriticalbifurcation, we obtain the noncoexistence of the periodic orbits andhomoclinic orbits and the existence of two or three heteroclinicorbits.