Coupled Van der Pol Networks
Dynamical Systems
2026-07-19 v1
Abstract
In this work, we provide a complete analytical characterization of amplitude modes in a nonlinear Van der Pol network. The phase condition presented in the paper fully classifies all possible configurations, leading to a finite set of discrete solutions. This result provides a complete description of the limit cycles, including all stable oscillatory states for arbitrary network size, without relying on approximate or iterative numerical schemes. In addition, we provide a constructive theorem that yields an iterative scheme for approximating solutions of the corresponding boundary-value problem.
Cite
@article{arxiv.2607.18337,
title = {Coupled Van der Pol Networks},
author = {O. Pokytnyi and O. Viatchaninov},
journal= {arXiv preprint arXiv:2607.18337},
year = {2026}
}