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Seminar: Applied/Biomath seminars

Speaker: Joel Zirkle Location: LD 002

Analyzing the Synchronization between Weakly Coupled Neurons

Synchronization is an important phenomenon in coupled self-sustained oscillators, and is the subject of intense research in applied dynamical systems. One can view neurons as oscillators and then study the synchronization in networks of coupled neurons. Synchronization allows neurons to group together to perform various tasks that would otherwise be impossible individually. For example, there is evidence that synchronization is related to memory formation, motor control, and perception.

I will talk about the mathematical analysis of neural synchrony and my recent research in the analysis of how synchronous phenomena develop in time, when the connections between oscillators are modulated. More specifically, I consider two neurons, described using the Morris-Lecar model, coupled via excitatory synapses. To consider synchronization, the phases of the cells and then a first-return map are constructed. For biological reasons, frequent but short desynchronizations can be beneficial (as opposed to infrequent but longer desynchronizations). I will discuss the results of a recent study showing how these short desynchronizations can be prevalent. I will also discuss the results of my research, showing how plasticity in the synapses tends to encourage shorter desynchronizations in the system, similar to experimental observations.

Organizer: J. Barber