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arXiv · 2607.18337

Coupled Van der Pol Networks

O. Pokytnyi·O. Viatchaninov
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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.

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O. Pokytnyi, O. Viatchaninov. 2026-07-19. Coupled Van der Pol Networks. https://arxiv.org/abs/2607.18337

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