2023/08/14 by Youngmin Park, Park, Youngmin, Dan Wilson +1 · 1 citation
Neuroscience · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Biological sciences #FOS: Physical sciences #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Spectroscopy and Quantum Chemical Studies #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2308.07425
openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \ypas 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.