Research On The Property Of Neuronal Network With Izhikevich Model

Brain could be the most complex and important organ in the human body.It has been widely investigated in the past decades.The ever-increasing morbidity of brain diseases makes the investigation on this topic significant in both biolo-gy and medicine.In the past twenty years,many countries put forward their own Brain Project and accelerate the investigation on this area.However,although it has been feasible for us to investigate the neurons in cellular and even molecular levels,there still remains many problems for biological experiments to analyze the behaviors of such a complex and huge system.Fortunately,computational neu-roscience was born at the right moment.With mathematical models and the idea of complex networks,we are able to simulate part of the behaviors of real cor-tex.The simulation could be an important supplement for biological experiments Our work is based on the idea of computational neuroscience.We build simple neuronal networks,simulate and discuss part of the behaviors of real cortex with computer programs.We hope our work would help to improve our comprehension over the operating modes of real cortex Our simulations are based on the Izhikevich neuronal model,a model with two differential equations simplified from the four-dimensional Hodgkin-Huxley neuronal model.Because of its simpleness and universality,we choose Izhikevich neuronal model to build neuronal networks.Meanwhile,we introduce the idea of short-term plasticity,which suggests that synapses could adjust their strength according to the behaviors of neurons.Specifically,we introduce the Tsodyks-Uziel-Markram(TUM)model to simulate the consumption and accumulation of neurotransmitters.With the help of these mathematical models,we build some simple neuronal networks and observe the behaviors of these networks under d-ifferent external inputs.In our investigation,we mainly focus on the inhibitory neurons.They can provide inhibitory currents in the network and help to con-trol the activity level of the system.We are interested in how they operate in the neuronal networks and the role they play in the collective behaviors of neuronal networks In our simulations,we first investigate on the synchronization of Izhikevich neuronal networks with short-term plasticity.We make comparative studies by considering the inhibitory neurons could fire either spontaneously or not in the network.We further discuss the role inhibitory neurons play in the synchronization of neuronal networks.Furthermore,we also investigate the effects of inhibitory neurons in the feedback and feedforward microcircuits with the help of Izhikevich neuronal model The structure and innovation of this thesis are as follows Chapter 1:In this chapter,we first review the current status of brain science and introduce the importance of computational neuroscience.Secondly,we intro-duce the main elements to focus on in the investigation of computational neuro-science:the neurons,the synapses and the networks.We introduce some neuronal models and introduce the idea of synaptic plasticity.We also introduce the impor-tance of inhibitory neurons in this chapter Chapter 2:In this chapter,we investigate the synchronization in the neuronal networks with the help of Izhikevich neuronal model and TUM model.Our work follows the current discussion on the role inhibitory neurons play in the synchro-nization.Based on our comparative studies,we discuss the two-fold effects of inhibitory neurons on synchronization Chapter 3:In this chapter,we investigate the feedforward and feedback inhi-bition in the neuronal networks.In the investigation on feedforward microcircuits,we find that the inhibitory neurons could narrow the window for temporal sum-mation of signals and action in excitatory neurons.In the investigation on feed-back microcircuits,we observe the "winners-take-all" mechanism.We also have to point out that in the "winners-take-all" mechanism,the "winners" are not the neurons who receives the strongest external input,but the neurons who provide action potentials fastest Chapter 4:In this chapter,the contents of the researches listed in this thesis are briefly summarized.We also draw a prospect for possible follow-up works.