Firing patterns and fast–slow dynamics in an N-type LAM-based FitzHugh–Nagumo circuit.

The diversity of firing patterns and their bifurcation mechanisms of a neuron circuit are crucial for exploiting bionic applications. This paper constructs an N-type locally active memristor (LAM)-based FitzHugh–Nagumo (FHN) circuit by replacing the tunnel-diode in the original FHN circuit. Numerical simulations and hardware measurements reveal that the N-type LAM-based FHN circuit can reproduce rich neuromorphic firing patterns of quasi-periodic/periodic bursting behaviors and chaotic/periodic spiking behaviors. The bursting and spiking behaviors are triggered by a low-frequency stimulus and a high-frequency one, respectively. Besides, the fold and Hopf bifurcation sets are depicted. Then, the bifurcation mechanisms for the quasi-periodic and periodic bursting behaviors via Hopf/Hopf and Hopf/fold bifurcations are theoretically deduced by time-domain waveform and equilibrium trajectory. The numerical results and hardware experiments exhibit the effectiveness of the proposed memristive FHN circuit in reproducing abundant firing patterns of bursting and spiking behaviors. • An N-type locally active memristor-based FHN circuit is first built by replace the tunnel-diode. • Fast–slow dynamics versus to high-frequency and low-frequency stimuli are explored. • Bifurcation mechanisms for quasi-periodic and periodic bursting behaviors are deduced. • Hardware experiments are executed to validate the generation of spiking and bursting behaviors. [ABSTRACT FROM AUTHOR]