Stability of the synchronization manifold in nearest neighbors non identical van der Pol-like oscillators

TL;DR

This paper analyzes the stability of synchronization in networks of coupled van der Pol oscillators, demonstrating that synchronization can be stable despite parameter variations, using the Master Stability Function and Kuramoto order parameter methods.

Contribution

It introduces a combined approach using the Master Stability Function and Kuramoto order parameter to determine stability boundaries in non-identical van der Pol oscillator networks.

Findings

Synchronization is achievable in large coupled van der Pol systems.

Stability persists despite parameter heterogeneity.

Analytical methods effectively predict synchronization boundaries.

Abstract

We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit cycles van der Pol oscillators. Such model represents, for instance, coherent oscillations in biological systems through the case of an enzymatic-substrate reaction with ferroelectric behavior in brain waves model. The ring and open-ended chain of identical and non-identical oscillators are considered separately. By using the Master Stability Function approach (for the identical case) and the complex Kuramoto order parameter (for the non-identical case), we derive the stability boundaries of the synchronized manifold. We have found that synchronization occurs in a system of many coupled modified van der Pol oscillators and it is stable even in presence of a spread of parameters.