Transition and bifurcation mechanism of firing activities in memristor synapse-coupled Hindmarsh–Rose bi-neuron model

Memristor , especially the locally active one, is widely used in emulating the synapse-inspired activities in neural networks , in which the connection between memristor properties and neuronal electrical activities requires further investigation. In this paper, a bi-neuron model is constructed by bi-directionally connecting a locally active memristor between the membrane potentials of two deterministic 3D HR neuron models. Complex spiking/bursting firing activities and their transitions are disclosed under different memristor control parameters. The bifurcation mechanisms of the revealed synchronous and asynchronous firing activities are explored inside each individual neuron by taking the externally input state variables as modulation parameters. These results demonstrate the crucial effect of the locally active memristor synapse on firing activities of its coupled network. FPGA-based digital circuit experiment is finally performed to verify the numerical results. This research is beneficial to understanding, control and application of firing activities in neural networks . • An LSCN model is proposed by two 3D HR models via LAM memristor coupling. • The connection between memristor features and neural electrical activities is investigated. • Bifurcation mechanism of neural electrical activities is interpreted.