Firing and synchronous of two memristive neurons

As a nonlinear circuit component, memristor can be utilized to simulate neural discharging activities in biological neural networks with synapses and neurons. In this paper, a polynomial memristor model is presented, with subcomponents acting on Fitzhugh–Nagumo (FN) and Hindmarsh–Rose (HR) neurons respectively to form new artificial neurons. One new memristor-based HR neuron simulates the electromagnetic induction environment of a 3D HR neuron, where the formation mechanism of firing activities is analyzed by fast-and-slow subsystems analysis method and nonlinear theory; the other is activated to couple the above memristor-based HR neuron with the FN neuron. The complex dynamics and the peak synchronous firing of the two different neurons are then further explored, and their synchronous firing is tested and verified based on their interspike intervals bifurcation diagrams, phase differences, and firing synchronization errors. This work provides necessary support for further exploring the complex dynamic mechanisms of biomimetic neurons.