Synchronization And Lyapunov Exponents Of Self-sustained Neural Oscillators Driven By Strong Noise

Synchronization is found in the same region or different regions of the cortex. Experiments have also demonstrated a remarkable reliability of repetitive spike sequences in neocortical neurons in response to repeated fluctuating stimuli, which is a feature not observed in response to constant input currents. In order to explain this phenomenon and the mechanism of neural encoding, scientists have done so many work. Previous researches give some theoretical explanation about the mechanism of the synchronization phenomenon. But these researches focus on the response of weak stimulus. In realistic situations, the neurons transmit signals on the basis of strongly stochastic spike series, and the neural signals are not weak but strong. These strong and stochastic neural signals can be discussed through the effect of strong stochastic noise. In this Letter, we demonstrate the behavior of strong noise driven neurons and calculate the leading Lyapunov exponents. We find strong noise can drive the oscillatory neurons with different initial condition to synchronize, and the numerical Lyapunove exponents still remain positive.In the first chapter, we demonstrate the effect of noise on the excitable, oscillating and chaotic systems.In the second chapter, we simply demonstrate the behavior of neural electrical discharge, and the building of neuron model. Then we focus on the behavior of the strong noise on the Adelman-Fitzhugh (AF) model, and calculate the leading Lyapunov exponents numerically. In previous research, people focus on the effect of weak noise on the neurons, and find when synchronization occurs, the leading Lyapunov exponents is negative. But in realistic situations, the stimulus should not be weak but strong. So we demonstrate the effect of strong noise on the oscillatory AF neurons. Under common strong noise, synchronization occurs for identical neurons with different initial conditions. More importantly, the spike series under strong noise seem more stochastic in contrast to the regular ones under weak noise. This result agrees with the experimental observation well. The leading Lyapunov exponents remain positive and increase with the noise intensity.In the third chapter, we demonstrate the behavior of a sub-threshold oscillatory neuron model forced by periodic stimulus. When the amplitude of the signal is strong enough, the output of the neuron have the same frequency with the input. Under different initial conditions, synchronization occurs. When the amplitude of the input signal increase, there are burst phenomenon. Increase the amplitude continually, the spike numbers in a burst increase as well. This is a new phenomenon, maybe we can find some cue about the signal transfer and encode of neuron.The forth chapter is the conclusion.