The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues

Abstract EN

The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems.

The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given.

The existence or nonexistence of saddle-node bifurcation surfaces is obtained.

Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases.

Moreover, the methods adopted in this paper can be extended to a higher dimensional system.