Color Noise Induced Coherence Resonance In Neural Networks And Spiral Waves

Neuron is a component unit of nervous system. The nervous system which has a specific physiological function is composed of billions of coupled neurons by various junctions. It is a kind of highly nonlinear system. Because of the complexity of the nervous system, nonlinear scientific theory and research method are gradually introduced in the research of nerve science. The focus of recent studies about nervous system has shifted to neuronal network from the single neuron.Realization of nervous system physiology function is dependent on the various activities of the neuron, which mainly is electric activity of neuron. The research about a large number of neurons by experiment with the great workload and is lack operability. So in the research of neuronal network, the simulation study of neuron model usually be used to guide the intensive studies of nervous system, which has the advantages of simple operation, convenient observation of data. Noise in nervous system may arise from many ways, such as molecular thermal fluctuation in the neighbor aera, the random open or close of ionic channels on the cell membrane, the quasi-random release of presynaptic synaptic vesicles by the synapses, the changes of membrane parameters induced by cell membrane endocytosis and exocytosis, or even the random synaptic input by the neghor nerons, which make the whole enviroment filled with noise. So, it is particularly important in research that about the influence of noise in neuronal system. The constructive effects of noise in nonlinear systerms is stochastic resonance (SR), it is that the existence of noise can evoke the best correlation between a weak external signe and the response of the nonlinear system. Moreover, noise alone is also able to enhance the order of nonlinear system, which has been termed coherence resonance (CR). In the researchs of nonlinear network, a series of spatiotemporal patterns have been observed induced by noise, such as spiral wave. In many studies about coherence resonance and spatiotemporal patterns, fluctuations are typically considered as the white noise. But in fact, the white noise is in the nonexistence, the colored noise introducing the correlation time is more practical to describe the effect of real noise. Gaussian colored noise induced spatial patterns and spatial coherence resonances in a two-dimensional square lattice neuronal network composed of Morris-Lecar neurons are studied in this paper. Each neuron is at resting state near a saddle-node bifurcation on invariant circle, coupled to its nearest neighbors by electronic coupling.The coupling strength is chosen as different levels to describe different neuronal network. The noise intensity and correlation time of the noise can decide the Gaussian colored noise. Record the membrane potential of each neuron in time under different noise, reflecting the spatiotemporal patterns of the neuronal network.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity. To quantify the differences between the spiral waves and the disordered spatial structures,we calculated the spatial structure function and signal-to-noise ratio (SNR). Compared the SNR with the spiral wave patterns, it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered, respectively. SNR manifest multiple local maximal peaks, indicating that the colored noise can induce multiple spatial coherence resonances in neuronal network. The maximal SNR values decrease as the correlation time of the noise increases. It shows that colored noise suppress the effect of CR with increasing correlation time of the noise.In addition, the transitions between spiral waves and disordered patterns are found under one specific noise intensity. The SNR curves show multiple local maximal values with the time, indicating that the colored noise can induce multiple coherence resonances at time scales in neuronal network. These results will lead us to further understand the spatial behavior of neuronal network.