Quasi-period, periodic bursting and bifurcations in memristor-based FitzHugh-Nagumo circuit

Abstract

A third-order non-autonomous memristor-based FitzHugh-Nagumo (FHN) circuit is proposed through introducing a memristor emulator to realize the nonlinear function of the membrane voltage in the FHN model. This memristive FHN model possesses two slow time-scales, i.e. the external forcing current and the memristor inner state variable, and quasi-periodic, periodic bursting, and periodic behaviors are numerically revealed. The mechanism of the two-slow-time-scale-dependent periodic bursting dynamics is explored through using graphical method. Moreover, with the evolution of time, the equilibrium point of the memristive FHN circuit evolves between no equilibrium and line equilibrium point, and the stabilities of the line equilibrium point are highly related to the memristor initial condition. Consequently, the exhibited dynamics can be adjusted not only by tuning the system parameters, i.e. the forcing amplitude and frequency, but also by changing the memristor initial condition. The coexistence of multiple bifurcation modes are also found in some system parameter regions. Finally, a simulated circuit model is designed and PSIM circuit simulations are performed to confirm the numerical simulations. The presented memristive FHN circuit can enrich the family of memristor-based FHN circuits and their exhibited firing dynamics.