Distance dependent competitive interactions in a frustrated network of mobile agents

TL;DR

This paper explores how spatially moving agents with distance-dependent attractive and repulsive interactions exhibit diverse collective behaviors, including synchronization and extreme events, with dynamics mapped across coupling parameters.

Contribution

It introduces a model of mobile agents with distance-dependent competing interactions and analyzes the resulting complex collective dynamics, including an analytical study of synchronization.

Findings

Diverse collective behaviors observed, including synchronization, oscillations, and extreme events.

Dynamics mapped in the coupling parameter space, showing transitions between states.

Analytical results for synchronization agree with numerical simulations.

Abstract

Diverse collective dynamics emerge in dynamical systems interacting on top of complex network architectures. Along this line of research, temporal network has come out to be one of the most promising network platforms to investigate. Especially, such network with spatially moving agents has been established to be capable of modelling a number of practical instances. In this paper, we examine the dynamical outcomes of moving agents interacting based upon their physical proximity. For this, we particularly emphasize on the impact of competing interactions among the agents depending on their physical distance. We specifically assume attractive coupling between agents which are staying apart from each other, whereas we adopt repulsive interaction for agents that are sufficiently close in space. With this set-up, we consider two types of coupling configurations, symmetry-breaking and symmetry-preserving couplings. We encounter variants of collective dynamics ranging from synchronization, inhomogeneous small oscillation to cluster state and extreme events while changing the attractive and repulsive coupling strengths. We have been able to map all these dynamical behaviors in the coupling parameter space. Complete synchronization being the most desired state in absence of repulsive coupling, we present an analytical study for this scenario that agrees well with the numerical results.