Study on nonlinear characteristics of two synchronizing uncoupled Hindmarsh-Rose neurons

Abstract

Modulating the current input of two uncoupled Hindmarsh-Rose neurons by using the membrane potential of Hindmarsh-Rose neuron under different initial conditions, the evolution mechanism of synchronization process of the two neurons is revealed by analyzing interspike interval sequences. When periodic stimulation is u sed, the full synchronization is realized in two identical neurons, and the sync hronized response of modulated neurons can be different from the stimulation sig nal; and phase synchronization can be obtained in two neurons with different par ameters:two neurons with small parameter mismatch can be synchronized to the per iodic response different from the stimulation signal, and two neurons with big p arameter mismatch can only be synchronized to the response in phase synchronizat ion with stimulation signal. When chaotic stimulation is used, two systems can o nly be synchronized to the response being in phase synchronization with stimulat ion signal. Obviously, chaotic stimulation is more helpful in encoding and deco ding information. Analyzing the relation between the largest condition Lyapunov exponents and the stimulation strength shows that when the largest condition Lya punov exponents of the two systems are both negative is the necessary condition for synchronization. The chaotic stimulation signal can more easily synchronize two neurons than periodic stimulation signal, implying that the effect of chaoti c stimulation is stronger than periodic one, and the experiments also confirm th is conclusion.