Study On Synchronism Of Coupling Neurons Neurons Induced By Bounded Noise And Delayed Feedback

This paper mainly studied synchronism of coupling neurons induced by bounded noise and time delayed feedback. Firstly, the thesis elaborates the basic theory and methods of stochastic dynamic in statistical physics. Secondly, F-N model and some physical concepts are introduced. Finally, studying synchro-nism of coupling neurons induced by bounded noise and time delayed feedback with F-N model.We introduce nonlinear time delayed feedback and bounded noise into F-N model, because bounded noise is more truthful than white noise in the nature, and this combination of bounded noise and time delayed feedback hadn’t been applied into the study of synchronization control, this is an innovation point of this thesis. Both the correlation time of bounded noise and delay time influence time scale of oscillation, thus making a difference to synchronization of oscilla-tions. So the interaction of correlation time and delay time is the core issue in this thesis.To better understand the function of bounded noise in synchronization control, firstly, we study F-N model driven by bounded noise without control, knowing that bounded noise intensity A and the strength of coupling C have an influence on the time scale. On that basis, we expand the study into F-N model driven by bounded noise with control, then studying mainly the effect of correlation time Tc and delay time Td of bounded noise on synchronization effect between two neurons, finally, comparing the results of bounded noise and white noise serving as driving force.We find the graphs of frequency synchronization and phase synchroniza-tion present overlapping on Tc≈1. namely graphic trend appears difference with Td increasing, the difference enhances with Td further increasing. Frequency synchronization and phase synchronization decrease and are suppressed with correlation time Tc increases. During studying the influence of delay time Td on synchronization we find the two kinds of synchronization are enhanced or sup-pressed. It is this innovation that studying the synchronization of two coupled neurons by bounded noise serving as driving force, we find the synchronization of two coupled neurons is almost unaffected by white noise serving as driving force under the same parameters, but the synchronization of two coupled neurons is obviously suppressed at delay time Td≈2, the suppression effect dies down with the strength of coupling C enhanced gradually, and the effect will die out when the strength of coupling is enhanced to a certain degree(C=0.6), at this time we also get the perfect synchronization(γ1,1= RISI=1).