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NJIT Mathematical Biology Seminar

Tuesday, October 7, 2008, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Loss of synchrony in non-weakly coupled inhibitory netowrks of type-I oscillators

Myongkeun Oh

Department of Mathematical Sciences, NJIT

Inhibitory networks of weakly-coupled type-I model neurons can exhibit a transition from synchronous dynamics to alternating order ("leap-frog") activity in response to an increase in synaptic coupling strength, whereby the spiking order of the coupled model cells changes in each cycle of the oscillation. This loss of synchrony is a result of a transient suppression of the postsynaptic cell below its excitability threshold, the saddle-node bifurcation, allowing the pre-synaptic cell to bypass it along the limit cycle trajectory. Here we describe the phase-space geometry of alternating-order activity, and examine the conditions for its existence and stability. We find that non-zero synaptic decay time is crucial for leap-frog firing in a network of limit cycle oscillators, and that the change in the firing order relies on the slow dynamics of each cell along the sub-threshold portion of the limit cycle. However, we show that order alternation can also be obtained in a purely pulse-coupled network of non-limit cycle oscillators such as quadratic integrate-and-fire model cells with asymmetric threshold and reset values. These results contribute to a better understanding of highly non-trivial synchronization properties of excitable cells, important for the study of neural circuit dynamics.