Resonance Phenomeon Of The Morris-Lecar Model

Neuron is fundamental and functional unit of nerve system in animals. There are numerous neurons in nerve system. The function of neuron is information processing, including receiving, integrating and transmissing. Neural ensemble achieves analytical function to create consciousness by information exchanged among the neurons. And noise is universal in our environment, there are many researches expound that noise has significant impact on the information integration in the single neuron and information transmission in the neural ensemble, so studying the influence of noise on neuron is meaningful for understanding the coding and transmission mechanism in our brains.The author modifies the Morris-Lecar model by embedding a small parameter using the Tikhonov's singular perturbation theory and finds its bifurcation points. Then give the resonance analysis by changing the amplitude and frequency of the period stimulus. Every system has its intrinsical frequency. When the frequency of the input signals approach this frequency, the model appears resonance. According to this, we find several classes of spiking.By applying noise alone and noise and weak period signal together in single Morris-Lecar model and two coupled neurons, we study the coherence resonance and stochastic resonance, and get a conclusion that the induced noise has a remarkable function on the information coding.Comparing to the occurrence of Canard in Morris-Lecar model, this paper puts forward a necessary condition of it.And finally, the author discusses the influence of high frequency signal in a single Morris-Lecar model, i.e. vibrational coherence, and summarizes the effect of it by changing the amplitude and frequency of high frequency signal. Compared to the influence of high frequency signal and noise in information coding, the author finds that they can substitute each other partly.Basing on the researches above, we could understand the influence of noise in the nerve system more clearly. The results can provide theoretical guidance for the research of noise in human body.