Synchronization in memristive HR neurons with hidden coexisting firing and lower energy under electrical and magnetic coupling

Abstract

Employing memristors to mimic biological synapses and to describe electromagnetic induction effects attracts much attention in current researches. In this paper, a memristive Hindmarsh–Rose neuron model is proposed by using an electromagnetic inductive current involving quadratic memconductance to replace the adaptive current in the classical 3-D HR model. The memristive neuron shows hidden firing and coexisting state. The energy function of memristive neuron is deduced by the generalized Hamiltonian formalism. In particular, two memristive neurons with irregular firing reach phase synchronization under the electrical coupling, while achieve complete synchronization under the magnetic coupling. The coupled neurons operate with economy energy in the region of whether complete synchronization or phase synchronization. Corresponding results are further demonstrated by designing digital circuit. These theoretical investigations can better choose appropriate model to explore dynamics of larger-scale neuronal network.