# Long-range interaction induced collective dynamical behaviors

## TL;DR

This paper explores how long-range interactions, especially with repulsive coupling, influence collective behaviors in coupled oscillators, revealing state transitions and stability conditions.

## Contribution

It introduces a detailed analysis of the effects of repulsive and symmetry-breaking couplings on collective dynamics in long-range oscillator systems.

## Key findings

- Repulsive coupling induces a swing of the synchronized state.
- Increasing disorder diminishes synchronization.
- Analytical stability conditions for various states are derived.

## Abstract

Long-range interacting systems are omnipresent in nature. We investigate here the collective dynamical behavior in a long-range interacting system consisting of coupled Stuart-Landau limit cycle oscillators. In particular, we analyze the impact of a repulsive coupling along with symmetry breaking coupling. We report that the addition of repulsive coupling of sufficient strength can induce a swing of the synchronized state which will start disappearing with an increasing disorder as a function of the repulsive coupling. We also deduce analytical stability conditions for the oscillatory states including synchronized state, solitary state, two-cluster state as well as oscillation death state. Finally, we have also analyzed the effect of power-law exponent on the observed dynamical states.