Firing activities induced by memristive autapse in Fitzhugh–Nagumo neuron with time delay

Due to the natural non-volatility and distinctive plasticity, memristors are considered as ideal devices to mimic biological synapses. In this study, an autapse which is implemented with a locally active memristor, is introduced into Fitzhugh–Nagumo neuron and thus a new neuron model is established. The local stability of the neuron model with and without time delay is analyzed, respectively. Four coexisting firing patterns, including chaotic spiking, periodic spiking, periodic bursting and chaotic bursting, dependent on the memristor initial values, are explored. We find that the neuron has four regular attraction basins and its firing pattern can be regulated by choosing appropriate initial values. The time delay has an important effect on firing activities and the neuron model transits from periodic spiking, to chaotic bursting, and then to chaotic spiking with the increase of the time delay. Furthermore, the influence of the autaptic intensity on firing activities of the neuron is also revealed. In order to verify the complex firing activities, a neuron circuit is constructed and circuit simulations are performed.