Bruno Gonçalves (Universidade do Porto)
We study an explicit periodically forced FitzHugh–Nagumo equation in the singularly perturbed regime. Using geometric singular perturbation theory, we analyse the associated return map and show that for large forcing amplitudes the system undergoes a transition from regular to chaotic dynamics as the perturbation amplitude increases. For sufficiently small perturbation amplitudes, the dynamics are organised by an attracting invariant torus. Beyond a critical threshold, the return map satisfies the geometric conditions of Wang–Young rank-one theory, yielding strange attractors with positive Lyapunov exponents and SRB measures for a positive Lebesgue measure set of parameter values. These results provide a rigorous mechanism for the emergence of observable chaos in periodically forced relaxation oscillators. We illustrate our results with numerical simulations.
Poster