Initial-induced coexisting and synchronous firing activities in memristor synapse-coupled Morris-Lecar bi-neuron network

A memristor synapse with threshold memductance is employed to couple two neurons for representation of the electromagnetic induction effect triggered by their membrane potential difference. This paper presents a memristor synapse-coupled bi-neuron network by bidirectionally coupling two three-dimensional heterogeneous or homogeneous Morris-Lecar neurons with such a memristor synapse. The memristive bi-neuron network possesses a line equilibrium set with its stability related to the induction coefficient and memristor initial value. Coexisting firing activities in the heterogeneous memristive bi-neuron network are explored using bifurcation plots, phase plots, and time sequences, upon which the initial-induced infinitely many firing patterns including hyperchaotic, chaotic, and periodic bursting and tonic-spiking patterns are disclosed, indicating the emergence of the initial-induced extreme multistability. Furthermore, synchronous firing activities in homogeneous memristive bi-neuron network are investigated using the time sequences, synchronization transition states, and mean synchronized errors. The results demonstrate that the synchronous firing activities are associated with the induction coefficient and specially associated with the initial values of memristor synapse and coupling neurons. Finally, an FPGA-based electronic bi-neuron network is designed to experimentally confirm the memristor initial-induced coexisting firing activities.