Memristor-induced mode transitions and extreme multistability in a map-based neuron model

Because of the advent of discrete memristor, memristor effect in discrete map has become the important subject deserving discussion. To this end, this paper constructs a memristor-based neuron model considering magnetic induction by combining an existing map-based neuron model and a discrete memristor with absolute value nonlinear memductance. Taking the coupling strength and initial state of the memristor as variables, complex mode transition behaviors induced by the introduced memristor are disclosed using numerical methods, including spiking-bursting behaviors, mode transition behaviors, and hyperchaotic spiking behaviors. In particular, all of these behaviors are greatly dependent on the memristor initial state, resulting in the existence of extreme multistability in the memristive neuron model. Therefore, this memristive neuron model can be used to effectively imitate the magnetic induction effects when complex mode transition behaviors appear in the neuronal action potential. Besides, an FPGA-based hardware platform is developed for implementing the memristive neuron model and various spiking-bursting sequences are experimentally captured therein. The results show that when biophysical memory effect is present, the memristive neuron model can better represent the firing activities of biological neurons than the original map-based neuron model.