Heterogeneous Coupling Arrangement Synchronization Of Different Neuron

Synchronization has a pivotal role in the study of nonlinear systems, nonlinear systems as one neuron system also requires in-depth study of the synchronization. In the biomedical community has been shown that the human brain synchronization of neurons leads to a number of diseases such as epilepsy, Parkinson’s generation, so the study of neuronal synchronization is necessary. As good abstract neuron model, FHN and HR neuron model is one of the best studied.In order to study the case of synchronous neural network, this paper takes a one-dimensional ring coupling ring network heterogeneity FitzHugh-Nagumo (FHN) neurons and Hindmarsh-Rose (HR) neurons for the study, discuss the spatial parameters of the different distributions under the influence of synchronization. For FHN neurons, we consider the frequency synchronization of neurons, the HR neurons, we consider the phase synchronization of neurons. Studies have shown that neurons in different spatial distributions of different parameters have some influence on the synchronization of the network. Overall, when the small number of neurons in the study, for FHN neurons, when the network to satisfy the high and low frequency of neurons staggered way, the network easily sync to synchronize the smaller the required minimum coupling strength; and neuronal network to satisfy the focus groups arranged by frequency, the network is not easy to sync, reach the minimum required to synchronize a large coupling strength. For HR neurons, when the parameters satisfy the heterogeneity of small decentralized arrangement of neurons, the network easily sync; when the parameters satisfy the small heterogeneous groups of neurons centralized arrangement, the network is not easy to sync. When the number of neurons in many studies, we give the characterization of the arrangement characteristic quantity for characterization network arrangement, and gives the relationship between volume and characterize critical coupling strength.In FHN Neuron study, we may be bifurcated process synchronization by the frequency distribution of synchronization differences impact on some analysis of this space. Analysts pointed out that when the spatial arrangement in line with the characteristics of high and low frequency staggered, frequency synchronization of neurons is synchronized explosive, that the coupling strength reaches a certain value, the frequency of all neurons also reached the same value, which reached frequency synchronization In this case the synchronization effect is better. When a small high-frequency parameters between neurons are arranged in groups each of these neighboring neurons preferentially pairwise synchronization, and finally when the coupling strength becomes larger when the synchronization between two neurons to reach a common frequency synchronization state, in which case, synchronization effect is poor.