| Siyuan Xing |
| Department of Mechanical Engineering California Polytechnic State University San Luis Obispo, CA, 93407, USA |
We perform the global analysis of periodic and homoclinic orbits in the Rossler system using a constructed implicit mapping structure. Through the continuation of equal-eigenvalue curves, we find biparametric folding-fan structures of periodic motions in the Rossler system. The rivet of the fan is associated with infinitely many homoclinic orbits. We also present a double-spiral bifurcation diagram of periodic motions, where infinitely many homoclinic orbits to Shilnikov saddle-focus coexist. In the end, we illustrate several primary and secondary homoclinic orbits.