Heterogeneous and homogeneous extreme multistability in a dual-memristor FHN circuit considering magnetic and electric field effects

The memristor-based neuron circuit considering the magnetic field effect is prone to heterogeneous extreme multistability (EM). However, the electric field effect represented by a charge-controlled memristor can also act on the neuron circuit, causing unusual nonlinear phenomena. To reveal the dynamical effects of magnetic and electric fields on biological neurons, this study proposes a novel non-autonomous dual-memristor FHN circuit considering magnetic and electric field effects. It is achieved by introducing a charge-controlled memristor representing the electric field effect into a single-memristor FHN circuit that considers only the magnetic field effect. The dual-memristor FHN circuit not only emerges the heterogeneous EM dependent on the initial states of the two memristors, but also presents the homogeneous EM whose dynamics can be boosted by the initial state offset of the charge-controlled memristor. The initial state-related bifurcation behaviors are numerically revealed, and the mechanism of homogeneous EM is theoretically interpreted. Further, a flux-charge model dependent on initial state parameters is established by feat of the incremental integral reconstruction, and then the initial state parameters-related stability and bifurcation behaviors are elaborated. Finally, digital implementations based on FPGA platform are provided to confirm the numerical simulations.