Study on synchrony of two uncoupled neurons under the neuron’s membrane potential stimulation

Abstract

The input current of two uncoupled Hindmarsh-Rose neurons under different initial conditions is modulated by the membrane potential of the Hindmarsh- Rose neuron; and the synchronization characteristics of the two uncoupled neurons are discussed by analyzing their membrane potentials and their inter spike interval (ISI) distribution. Under the stimulation of the neuron’s membrane potential whose discharge pattern is period or the chaos, the two uncoupled neurons under different initial conditions, whose parameter r (the parameter r is related to the membrane penetration of calcium ion, and reflects the changing speed of the slow adaptation current) is different or the same, can realize the full synchronization (state synchronization) or discharge synchronization (phase synchronization), and can only be synchronized to the discharge pattern of the stimulation neuron. The synchronization characteristics are mainly related to the discharge pattern and the strength of the stimulation neuron’s membrane potential, and are little related to the parameter r and the initial state of the two uncoupled neurons. This investigation shows the characteristics of the neuron’s membrane potential affecting the synchronization process of neurons, and the neurons’ discharge patterns and synchronization process can be adjusted and controlled by the discharge pattern and the strength of the stimulation neuron’s membrane potential. This result is helpful to study synchronization and encode of many neurons or neural network