School of Mathematical Sciences

N-Body Oscillator Interactions of Higher-Order Coupling Functions

Date(s)
Tuesday 30th April 2024 (14:00-15:00)
Contact
Event Convenor Contact: stephen.coombes@nottingham.ac.uk
Description
Speaker's Name: Youngmin Park
Speaker's Affiliation: University of Florida
Speaker's Research Theme(s): Mathematical neuroscience,
Abstract:
We introduce a method to identify phase equations that include N-body interactions for general coupled oscillators valid far beyond the weak coupling approximation. This strategy is an extension of the theory from [Park and Wilson, SIADS 20.3 (2021)] and yields coupling functions for N≥2 oscillators for arbitrary types of coupling (e.g., diffusive, gap-junction, chemical synaptic). These coupling functions enable the study of oscillator networks in terms of phase-locked states, whose stability can be determined using straightforward linear stability arguments. We demonstrate the utility of our approach with two examples. First, we use N=3 diffusively coupled complex Ginzburg-Landau (CGL) model and show that the loss of stability in its splay state occurs through a Hopf bifurcation \yp{as a function of non-weak diffusive coupling. Our reduction also captures asymptotic limit-cycle dynamics in the phase differences}. Second, we use N=3 realistic conductance-based thalamic neuron models and show that our method correctly predicts a loss in stability of a splay state for non-weak synaptic coupling. In both examples, our theory accurately captures model behaviors that weak and recent non-weak coupling theories can not.

Venue: Streamed in Maths A17
Online Conference Link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_MzNlNThjNzQtODE2Zi00YjA0LWEzMmQtODgzNDk0ODE3ZGMy%40thread.v2/0?context=%7b%22Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%22b2ea94a7-6542-496b-971d-e1941b5b59ad%22%7d

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

For all enquiries please visit:
www.nottingham.ac.uk/enquire