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A modified model of "integrate-and-fire neuron" has been developed to imitate cooperative functioning the neuronal networks (NN) of various brain structures. The components to simulate temporal dynamics immediately after-spike generation such as slow after-potentials, and threshold modulations were incorporated into neuron model. As first step, a realistic NN, accumulating knowledge about properties of the thalamic relay nucleus, and consisting of the modified "integrate-and-fire neurons" is created. The results of computer simulation are in agreement with neurobiological data about a dynamics of the thalamic neuronal activity during both waking and slow-wave sleep. Several new properties of activity dynamics were revealed such as a dependence of spatio-temporal parameters of neuron synchronization during the spindle wave on the local interaction architecture in the NN.