Relaxation Oscillations and the Entry-Exit Function in Multi-Dimensional Slow-Fast Systems

Ting-Hao Hsu, Shigui Ruan

For a slow-fast system of the form $\dot{p}=\epsilon f(p,z,\epsilon )+h(p,z,\epsilon )$, $\dot{z}=g(p,z,\epsilon )$ for $(p,z)\in {\mathbb{R}}^n\times {\mathbb{R}}^m$, we consider the scenario that the system has invar…