Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues

Abstract EN

By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the localcoordinate systems in the small tubular neighborhoods of theheteroclinic orbits, we study the bifurcation problems ofnontwisted heteroclinic loop with resonant eigenvalues.

Theexistence, numbers, and existence regions of 1-heteroclinic loop,1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two1-periodic orbits are obtained.

Meanwhile, we give thecorresponding bifurcation surfaces.