**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Thursday, January 11, 2018 — 3:30 PM EST

MC 6460

Hwayeon Ryu, Department of Mathematics, University of Hartford

Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays

We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider neurons in a globally inhibitory network where two distinct, one excitatory and one inhibitory, populations of neurons are coupled and interact with each other. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between two population. Numerical simulations are conducted to supplement and validate analytical results, and to analyze recent models for spindle sleep rhythms in thalamocortical networks, which have biologically motivated our study. In this talk, I will first introduce the network architecture and synaptic delays, and then describe how the geometric singular methods are used to construct the synchronous solutions. At the end of talk, the role of delays in producing synchronization will be discussed, which is supplemented by numerical simulation results.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.