# State-dependent effective interactions in oscillator networks through coupling functions with dead zones

## TL;DR

This paper investigates how coupling functions with dead zones influence the effective interactions in oscillator networks, revealing dynamic decoupling and evolving interactions based on phase configurations.

## Contribution

It formalizes the concepts of dead zones and effective interactions, showing how coupling functions shape and evolve network dynamics.

## Key findings

- Effective interactions can decouple oscillators in certain phase configurations.
- Effective coupling schemes are shaped by the structure of dead zones.
- Interactions can evolve over time along trajectories.

## Abstract

The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have "dead zones", that is, the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time.