Abstract
Electrical synapses and external stimuli can affect the exchange and propagation of field energy between neurons, and thus induce a variety of dynamics and electricity activities of the nervous system. This paper introduces a memristor synapse-coupled bi-HR neural network and investigates its discharge oscillation and phase synchronization based on energy method. It finds that the bi-HR network presents strong nonlinear phenomena such as anti-monotonicity and transient dynamics. And the bi-HR network shows complex electricity activities such as mixed-mode discharge and bursting discharge, which are demonstrated by the time evolution of membrane potential and Hamilton energy spectrum. Moreover, phase synchronization of the coupled neurons is studied and the synchronization characteristic relying on memristive synapse, magnetic field and external stimulus is explored by calculating Hamilton energy error, which coincides with phase difference and synchronization factor. Therefore, Hamiltonian energy is effective for investigating the firing pattern of neural system and the synchronization behavior of electrically coupled neurons.
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