\({n{:}m}\) Phase-Locking of Coupled Oscillators with Nonlinearities in Coupling Strength and Heterogeneity
Year: 2026
Type: article
Abstract: . We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The method can be used to determine the existence and stability of [Formula: see text] phase-locked states in a variety of forced or coupled biological oscillator models, including the nonradial isochron clock, a thalamic neural oscillator, and the van der Pol oscillator. The proposed scalar reduction successfully captures the emergence and disappearance of phase-locked states as a function of nonlinear coupling strength and nonlinear heterogeneity. We find that even small amounts of heterogeneity can significantly alter phase-locked states in ways that cannot be captured by assuming identical oscillators. The proposed method enables a reduction and analysis of high-dimensional systems of coupled oscillators in more biologically realistic settings.
DOI: 10.1137/25m1785976
Author: Youngmin Park
Institution: University of Florida
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4403780090