Volume 9 Supplement 1
Loss of synchrony in an inhibitory network of type-I oscillators
© Oh and Matveev; licensee BioMed Central Ltd. 2008
Published: 11 July 2008
Understanding the dynamics and synchronization of inhibitory neurons is a question of fundamental importance in neuroscience, since inhibitory networks play a crucial role in rhythmogenesis, both in invertebrate motor pattern generators  and in the mammalian hippocampus and neocortex . Invertebrate CPGs in particular often contain simple two-cell inhibitory sub-networks that play a crucial role in the control of rhythmic motor behaviors. Therefore, characterizing the dynamics of two-cell inhibitory networks is relevant for a better understanding of the rhythmic dynamic activity produced by central pattern generators and other inhibitory circuits.
We examine the phase-plane geometry of such order non-preserving dynamics, and find that it arises when the inhibition is sufficiently strong to allow a presynaptic cell to transiently suppress the postsynaptic cell below its excitability threshold (saddle-node on an invariant cycle bifurcation) in each cycle of the oscillation. Therefore, non-zero synaptic decay time is crucial for obtaining leap-frog spiking in a continuous system. However, we show that alternating-order spiking can also be obtained in an appropriately modified pulse-coupled integrate-and-fire network. Following the approach of Maran and Canavier , we show that the entire activity state bifurcation profile of the two-cell Morris-Lecar network can be completely characterized using the phase-resetting properties of each of the two cells, and describe the conditions on the phase resetting curve that lead to the loss of synchrony and the emergence of leap-frog spiking.
This work is partially supported by the National Science Foundation grant DMS-0417416
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