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Coupled Dynamics of Excitable Systems Base on Morris-Lecar Model

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Tutor: ZhaoTongJun
School: Hebei University of Technology
Course: Theoretical Physics
Keywords: Morris-Lecar model,Izhikevich modified model,balance potential,coupled synchroni
CLC: Q42
Type: Master's thesis
Year:  2011
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Abstract:
It¡¯s an important problem in neural science to study the dynamical behaviors of neuron as the foundation structure of neural system. In practical environments ,neurons are connected with other neurons through the synaptic . There are many types of models are built to research the dynamical mechanism of the single neuron include Hodgkin-Huxley£¨HH£© and Morris-Lecar models .Then we use the models which reflects neuron discharge as a node and construct a nerve networks with small-world connections, then study the influence between the coupled neurons.In this paper, we studied the neurons dynamical mechanism base on the two dimension Morris -Lecar neuron model .When one of the ion channels¡¯balance potential reach a certain threshold ,the neuron can be excited .The different balance potential of calcium can make the neuron excited with the different threshold of potassium balance potential . The balance potential of K+ had a correlation with in the nervous system. The ML model was modified by Izhikevich. Base on that , we simulated a single neuron have different bursters at the different balance potentials of K+ or Ca2+ channels . When the nervous system achieved many different bursters ,the banlance potential of calcium channel is smaller than the potassium.That when many different kinds of environment stimulates have effect on the neuron and lead the balance potentials are changed , the potassium is more stable than calcium. The coupled two or three different bursters of neurons is continued to study on the basis of single neuron research .There are many different bursters according to the different coupling strength .About that ,we know that the more neurons are coupled , the smaller coupling strength when the neurons are achieved synchronization .At the same time ,the burster types of the neurons are more than the single or two coupled neurons .In order to simulate a more realistic biological environment in which the neurons , we built a NW small-world network structure of the neurons, base on that we use the coupling strength make the number of ten to ninety neurons to have many different types of synchronization. With the expansion of the network of neurons , the coupling strength is in a decreasing trend when the neurons achieved a variety synchronization.We are able to study the neural dynamical features of the balance potential and the many neurons are coupled , which is important to understand the dynamical connection of neuron channels and the interaction influence of each neuron in the neural network in nature.
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