Research On The Neural Dynamic Considerations Based On Firing Rhythm

Based on the theory and method of nonlinear dynamics,a several of considerations of neural system are researched in this dissertation,such as,optimal selection of embedding parameters of phase space reconstruction for chaotic time series,the time-delayed feed back control on neural dynamic system,as well as the synchronization behavior of neural dynamic system with delayed coupling.The main works and results of this dissertation are summarized as follow:(1) An overview for development of dynamical system's chaotic time series,delay control,and system synchronization.A few of conception and dynamical characteristic of chaotic system are introduced by some typical dynamical system.(2) A novel algorithm is proposed to determine the embedding dimension and delay time;the delay time is firstly estimated with the method of average displacement of vector space;then,the embedding dimension of phase space reconstruction is estimated by one characters of chaotic attractor,i.e.based on that the distance of neighbor points of chaotic attractor will finally arrive at one saturated state with respecting to increasing time.The simulation results of application suggested that the proposed algorithm could effectively deal with the estimation of reconstruction parameters for nonlinear time series.(3) For an individual Hindmarsh-Rose neuron model with time delay,the dynamic considerations of firing depending on time delay are analyzed.It is found that delay timeτand synaptic intensityεhave an important role when neural firing pattern transform from one to another state.(4) With two group of the time delaysτand synaptic intensityεtogether,the neuronal chaotic firing behavior could been controlled to period-1 or period-3 acticities, respectively.(5) The study on the neuronal system's activities with delay coupling indicated that complete synchronization could be induced by appropriate time delaysτand coupling strengths c among coupled neurons,for example,a complete synchronous phenomenon appears for smaller coupling strengths under time delay.