# Weak-winner phase synchronization: A curious case of weak interactions

## TL;DR

This paper uncovers a novel synchronization state called 'weak-winner' where weakly coupled oscillators synchronize while strongly coupled ones do not, influenced by non-isochronicity and natural frequency, with broad implications across sciences.

## Contribution

It introduces the weak-winner phase synchronization phenomenon, explains its underlying mechanisms, and demonstrates its generic occurrence in various oscillator systems.

## Key findings

- Weak-winner synchronization occurs in coupled oscillators.
- Non-isochronicity influences synchronization patterns.
- The phenomenon is observed in both limit cycle and chaotic oscillators.

## Abstract

We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase synchronization while the strongly coupled oscillator pair does not. This intriguing "weak-winner" synchronization phenomenon can be explained by the interplay between non-isochronicity and natural frequency of the oscillator, as coupling strength is varied. Further, we present sufficient conditions under which the weak-winner phase synchronization can occur for limit cycle as well as chaotic oscillators. Employing model system from ecology as well as a paradigmatic model from physics, we demonstrate that this phenomenon is a generic feature for a large class of coupled oscillator systems. The realization of this peculiar yet quite generic weak-winner dynamics can have far reaching consequences in a wide range of scientific disciplines that deal with the phenomenon of phase synchronization. Our results also highlight the role of non-isochronicity (shear) as a fundamental feature of an oscillator in shaping the emergent dynamics.