Synchronization behavior in a memristive synapse-connected neuronal network

Synaptic plasticity is reflected in its ability to change the coupling strength according to the intensity of firing electrical activity in coupled neurons, which can also greatly affect synchronization behavior in neuronal networks. In this paper, synaptic plasticity is modeled based on the constitutive relationship of memristor, and it is only related to the membrane potential of two adjacent coupled neurons. Three types of neuronal network are proposed, that is, the ring network connected by electrical synapses, the ring network connected by mixed electrical and memristive synapses, and the ring network connected by memristive synapses. The firing activities of neurons and synchronization behavior of the three networks are comparatively studied. Direct or periodic forcing current is applied to the neurons in neuronal network, and the accumulated error and variable phase difference are calculated and used to detect synchronization state of the networks. Extensive simulation results confirm that periodic forcing current with appropriate angular frequency is more conducive to network synchronization than the direct one, and coupling strengths of electrical synapse and memristive synapse show different performance on network synchronization due to synaptic plasticity. The results will further deepen the understanding of synaptic plasticity and the synchronous behaviors of neuronal networks considering memristive synapse connection.