Study On Stochastic Response And Synchronous Performance In The Neural Networks With Small-world Character

That neuroscience (or brain science) rapidly rose was a significant event in the development of natural science in 20 century's ends 30's. As the main body of neuroscience, the neurobiology has already become one of most rapid front science in the life sciences development, it is a science studying human and animal's nervous system. Nervous system is a organism'regulative system, it can feel the information variety outside and inside economy, and conformity, process and respond to the information felt at same time. By nerve discharges pulse, nervous system may achieve a series of function ahead. In 20th century 50's, Hodgkin and Huxley put forward the notable HH equation, and expressed successfully nerve discharging electrochemistry mechanism.Complex networks is a better hot subject which was studied in recent years at home and abroad, involving a wide range. Since the pioneering work of two (namely Watts and Strogatz introduced small-world network model in 1998, Barabasi and Albert brought forward scale-free mode in 1999) appeared, it giving rise to an upsurge in the study of complex networks. Today the research to it is permeating from the mathematics and project technical science to a lot of different discipline such as sociology, physics, medicine and biology and so on.At present because the results of neurophysiology and complex networks show: the human brain real biological neural network system is a small-world network structure, we use HH model which reflects neuron discharge as a node and construct a artificial biology nerve networks with small-world connections, then study the second super-harmonic stochastic resonance , coherence resonance and synchronization in the network.This paper has mainly completed the following work:1.(1)When rewiring probability p, input signal frequency and amplitude A are invariable, along with coupling intensity c increases, the output signal-to-noise ratio curve of neural network drops, and the optimal super-second harmonic signal-to-noise ratio(SNR) also drops. This indicates that the ability of nervous system detects feeble super-harmonic signal drops as coupling intensity c increases. (2) When the strength D of noise is immovable (p, c, andωalso do not vary.), it isn't that the more stronger signal is ,the more bigger signal-to-noise ratio is, but the amplitude A has a optimal value AO to Hodgkin-Huxley(HH) neural network with small-world connections. The out SNR will reach to its maximum while A is equal to AO, this implies that system'ability detecting signal is most stronger at optimal value AO. These results further enrich the theory and application of stochastic resonance.2.(1)When the strength of noise is a certain limited value, the ordered degree of spike sequence may reach optimal, namely produces coherence resonance phenomena. (2) The minimum of coherence resonance coefficient cv isn't one, but many. This indicates that coherence resonance may occur in the different scale networks in which the numbers of neuron is specific. These studied results has certain referenced value to know the human brain study and the memory function and certain significance to understand and explain dynamics behavior such as order, regularity and synchronization and so on in the networks.3.(1)The synchronizing ability in the small-world nerve networks increases as addition probability p rises, this may be the reason which coupled function in networks is diffusive. (2) Noise can destroy the synchronization of nerve networks and make neurons becoming out-of-order in space. This is differ from that stochastic resonance, coherence resonance have optimal noise'strength D. it also show that the order of networks is not equal to its synchronization at the same time. (3) Couple among neurons may help neural networks synchronization. But coupled strength c can't get too big or small, otherwise it will induce that all neurons don't fire if c is too big; or that neurons haven't synchronization though they have firing pulse if c is too small. (4) Big networks is more easily synchronized than small networks, and the numbers of nearest neighbor may destroy the synchronization of networks if it is little many. These results can promote people know neuron encoding to information, and cognize and reveal the secret of brain working principle.