Burst patterns with Hopf bifurcation in a simplified FHN circuit

To theoretically and experimentally characterize the neuronal burst patterns, a simplified FitzHugh–Nagumo (FHN) circuit is developed by using two anti-parallel diodes to achieve nonlinearity, and its non-autonomous system model is thereby built. The simplified FHN system has a time-varying equilibrium point, whose position and stability change slowly over time. By employing numerical measures, periodic and quasi-periodic burst patterns along with quasi-periodic spike patterns are revealed in the simplified FHN system. Particularly, through constructing Hopf bifurcation set, the bifurcation mechanism for the burst behaviors is expounded theoretically. As a result, transitions between the spike and resting states are demonstrated, and Hopf/Hopf periodic and quasi-periodic burst patterns are identified. Finally, with the developed Multisim simulation model, analog circuit simulations and breadboard experiments are performed to confirm numerical results. Notably, the simplified FHN circuit is implemented with low-cost and no multiplier, which is of great significance for the construction of neuromorphic systems and contributes to the research and development of artificial neural networks.