Researches On Coherence Resonance Of The Neuronal Rulkov Model

The neuron is the basic function unit of nervous system and it is affected inevitably by all kinds of noise, such as randomness of cellular ion channels to open and close, chemical synapses to randomly release neurotransmitter and the random input current of other neurons.Traditional ideas believe that noise is harmful. However, the noise is necessary for the occurrence of some important kinetic process in nonlinear system and one of the important aspect is the phenomenon of stochastic resonance(SR) induced by noise, that is, noise can enhance system response to the external weak periodic signal.But in the nervous system, it don’t always have a signal input. At this point, there is another important phenomenon, which is coherence resonance(CR). CR refers to the phenomenon that there exists a finite strength of the noise at which the spike sequence is most regular. In recent years, many works on stochastic or coherence resonance of extended neuronal systems have been presented. But so far, the study of coherence resonance is concentrated on the function of Gaussian noise. However, noise with non-Gaussian distribution and bounded noise relativity appears more common in real physical and biological system. Hence, noise with non-Gaussian distribution and bounded noise could simulate noisy environment of life more exactly. In this paper, we will investigate the influence of non-Gaussian colored noise on the two-dimensional neural map and the firing performance and we will investigate the influence of non-Gaussian colored noise and bounded noise on the Rulkov neural map. The main research content is as follows:1. We investigate the coherence resonance influence of non-Gaussian colored noise on the chaotic Rulkov neuron model. Firstly,numerical simulation is studied by using numerical modeling for nonlinear equations. The system indicators related to the coherence resonance is obtained, such as,noise intensity、correlation time、non-Gaussian parameter. Secondly, Taking the coherence parameter R to measure the regularity of firing behavior, it is demonstrated that coherence parameter R has a pronounced minimum value with the noise intensity and the correlation time of non-Gaussian colored noise, which is so-called the phenomenon of coherence resonance(CR).2. We investigate the influence of non-Gaussian colored noise and bounded noise on the chaotic Rulkov neural map. By studying the non-Gaussian color noise excitation neurons discharge time series, we found that the intensity of colored Gaussian noise and non-Gaussian colored noise correlation time can affect the discharge behavior of the system. Then taking the coherence parameter R to measure the regularity of firing behavior, it is demonstrated that coherence parameter R has a pronounced minimum value with the noise intensity and the correlation time of non-Gaussian colored noise. This suggests that the chaotic Rulkov neural model can be induced to produce coherence resonance phenomenon by non-Gaussian color noise.Similarly, by using numerical simulation, it is concluded that neuronscan be induced to produce coherence resonance phenomenon bythe bounded noise.