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NJIT Mathematical Biology Seminar

Tuesday, February 17, 2009, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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The Activity Phase of Neurons in a Reciprocally Inhibitory Network

Xinxian Huang

Department of Mathematical Sciences, NJIT

In a network of two reciprocally inhibitory neurons, the firing time of one neuron (A) has an effect on the period of the other one (B), and vice versa. We investigate the phase of activity of neuron B as a function of the relative firing time of neuron A. We examine the conditions for the existence and stability of phase-locked activity. We determine the phase of activity of the mutually inhibitory network from information about two different feed-forward inhibitory networks. One characterizes the dependence of the cycle period of B on the relative firing time of A, and the other determines the relation between the phase of A and the period of B. In the special case that the period of B is linear function of the relative firing time of A, we obtain conditions on the existence and stability of phase-locked solution and describe the circumstances under which the solution is unique.