Geometric analysis of synchronization in neuronal networks with global inhibition and coupling delays

9 Jul 2018, 18:00
Holme Building/--The Refectory (University of Sydney)

Holme Building/--The Refectory

University of Sydney

Board: 501
Poster Presentation Other Mathematical Biology Poster Session


Dr Hwayeon Ryu (University of Hartford)


We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviours. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between the two populations, along with formulas for the periods of such synchronous solutions. Our results demonstrate that the presence of coupling delays in the network promotes synchronization. Numerical simulations are conducted to supplement and validate analytical results. We show the results carry over to a model for spindle sleep rhythms in thalamocortical networks, one of the biological systems which motivated our study. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms.

Primary authors

Dr Hwayeon Ryu (University of Hartford) Dr Sue Ann Campbell (University of Waterloo)

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