Hierarchical frequency-locking organization and quint points in a periodically driven FitzHugh-Nagumo neuron model

We uncover the global organization of resonance structures in a periodically driven FitzHugh-Nagumo neuron model. High-resolution Lyapunov diagrams with local-maxima (LM) classification expose a hierarchical network of Arnold tongues in parameter space. Frequency-locking regions emerge from quasiperiodic dynamics and extend into chaotic domains, following a period-adding organization consistent with Farey-tree ordering. Successive magnifications reveal multiscale embeddings of stable periodic structures containing quint points, where five periodic domains coalesce and satisfy local LM-adding relations. Basin-of-attraction analysis confirms multistability, including coexistence of periodic and chaotic attractors. In a neurostimulation context, these results show that periodic forcing can induce multiple coexisting frequency-locked firing regimes with distinct LM counts, providing a dynamical basis for stimulus-dependent neural encoding and selective response modulation.