Coupling dynamics and synchronization mode in driven FitzHugh–Nagumo neurons

We introduce a novel four-dimensional continuous-time nonautonomous dynamical system formed by coupling two sinusoidally driven FitzHugh–Nagumo (FHN) neurons. The study investigates dynamical behaviors and synchronization properties under three distinct scenarios: (i) coupling two identical chaotic systems, (ii) coupling a periodic system with a chaotic system, and (iii) coupling two identical periodic systems. Synchronization is analyzed in detail for the first two scenarios. In case (i), coupling suppresses chaotic behavior, inducing periodic dynamics characterized by intricate discontinuous spirals and self-similar shrimp-shaped periodic structures. Case (ii) reveals shrimp-shaped periodic structures and regions of coexisting attractors, showcasing the multistability inherent in nonlinear systems. For these two scenarios, we explore the transition from asynchronous states to intermittent and nearly synchronized states, driven by increasing coupling strength. The emergence of synchronization is interpreted in terms of the interaction between individual neuron dynamics and coupling. In case (iii), coupling completely stabilizes periodic dynamics, leading to an uniform periodic regime without chaotic behavior. Across all scenarios, increasing coupling strength in nonautononous FHN neuron models induces a transition from eventual finite-time synchronization events to stable coupling-driven synchronized states. We also demonstrate that, for two-coupled nonautonomous FHN neurons, the individual dynamics play a less significant role in the synchronization process compared to previous findings in coupled autonomous neuron models. This work highlights the complex interplay of coupling and intrinsic individual nonautonomous FHN neuron dynamics.