The Sufficient Study Of Postinhibitory Rebound In The Inhibitory Coupling Neuronal Networks

In this paper, the coupling neuronal network of e₁→s₁→e₂ and the modeling differential equations are studied from two aspects: the movement characteristics of neurons and modeling differential equations. At first, we construct the local singular solution of inhibited cell e₂ using ageometric singular perturbation approach under four hypotheses, and know how the parameters affect e₂ to happen postinhibitory rebound. Then we analyze the conditions of e₂ withpostinhibitory rebound from geometry view, the sufficient conditions(about parameters g_syn and β), under which the postinhibition rebound could happen, are given. Thus, whenever the parameters g_syn and β satisfy these conditions, cell e₂ will begin its postinhibitory rebound at the time T₀, which is the period of excited cell e₁ staying active state. The all course of e₂ postinhibitory rebound will end at some time Ï„>T₀. In the end, we check the correctness of sufficient conditions about modeling parameters g_syn and β by specific examples. This is useful in constructing the model of neuron networks.