The Activities Of Synchronization Of Neural Population In The Presence Of Stimulus

The electrochemical neurotransmitter on synapses can drive neighboring neurons tofire and modulate the coupling strength between the neighboring neurons. LTP（long–term potentiation）can affect the transmission of information and coupling strengthbetween neurons in the presence of stimulus, thus affects the efficiency of brain learning.Therefore，coupling strengths changing over time provide a more realistic picture ofsynchronization during learning in the brain.In this paper, as coupling strength changing over time, a phase transformationdynamics model in neural population is proposed in the presence of external stimulation.A probability density function is introduced to describe the state of neural populationand is expanded as Fourier series, then reduced to order parameter equation, which candescribe the level of synchronization of neural population activities.First, we studied the synchronization activity behaviors of neural population underthe effect of time-periodic coupling strength and with stimulation. we found that：theimpact of extracellular stimuli on the synchronous activity of neuronal oscillatorpopulation depends on stimulus intensity and stimulus frequency. Neuronal populationare influenced by the low-frequency weak stimulus very weak, high-frequency strongstimulus enhance synchronization activity of neuronal population. Meanwhile,synchronization behavior caused by mix stimulation is more evident than singlestimulation，and the length of synchronizing circle caused by mix stimulation is alsolonger than single stimulation. Secondly, based on Hebb learn rules, we introduced themodel of coupling strength changing over time to study neural population dynamic’sbehavior. We found that: high-frequency harmonic stimulus can produce theperiodically synchronized oscillations in the population of neuronal oscillators, and theperiod of synchronized oscillation is related to stimulus frequency. That is to say, thehigher the stimulus frequency, the higher the frequency of synchronized oscillation, andthe degree of synchronization increases with the increasing stimulus intensity. Stimulusfrequency information is encoded by the frequency of synchronous oscillation of neuralpopulation; stimulus intensity information is encoded by the degree of phasesynchronization.