Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation

Synapses can regulate the energy balance in the neural network. In this work, a two-neuron network is established by coupling two Morris-Lecar neurons using a memristor synapse. The periodic/hyperchaotic spiking-bursting patterns in the two-neuron network are portrayed using bifurcation plot, phase portrait, and time-domain waveform. The asynchronous behaviors exhibited by the numerical results show the difference of the inner field energy of individual neurons. To investigate the biophysical mechanism in the two-neuron network, the Hamiltonian energy function of a single neuron is derived by Helmholtz's theorem to equivalently describe its inner field energy, and the bioelectric activities are analyzed in combination with synchronization error functions. It is revealed that the initial state of memristor synapse can regulate the energy diversity in the two-neuron network and achieve the energy balance in the transient state. Two neurons firing in hyperchaotic pattern exchange field energy through the memristor synapse as a coupling channel until energy balance and complete synchronization. In the complete synchronization state, the memristor synapse is silent, which leads to the retrograding of hyperchaotic firing behaviors. Finally, an FPGA-based digital electronic two-neuron network is developed, and the experimental measurements well confirm the numerical simulations of bioelectric activities.