Fast-slow dynamics in a memristive ion channel-based bionic circuit

Electrophysiological properties of ion channels can influence the transport process of ions and the generation of firing patterns in an excitable biological neuron when applying an external stimulus and exceeding the excitable threshold. In this paper, a current stimulus is employed to emulate the external stimulus, and a second-order locally active memristor (LAM) is deployed to characterize the properties of ion channels. Then, a simple bionic circuit possessing the LAM, a capacitor, a DC voltage, and the current stimulus is constructed. Fast-slow dynamical effects of the current stimulus with low- and high-frequency are respectively explored. Numerical simulations disclose that the bionic circuit can generate bursting behaviors for the low-frequency current stimulus and spiking behaviors for the high-frequency current stimulus. Besides, fold and Hopf bifurcation sets are deduced and the bifurcation mechanisms for bursting behaviors are elaborated. Furthermore, the numerically simulated bursting and spiking behaviors are verified by PCB-based hardware experiments. These results reflect the feasibility of the bionic circuit in generating the firing patterns of spiking and bursting behaviors and the external current can be employed to regulate these firing patterns.