Hybrid dynamics in delay-coupled swarms with "mothership" networks

TL;DR

This paper investigates how delay and network heterogeneity, especially the inclusion of highly connected 'mothership' nodes, influence pattern formation and dynamics in swarm systems, revealing new behaviors and multi-stability.

Contribution

It introduces a generalized analysis of swarm patterns on heterogeneous networks with delays, highlighting the role of 'mothership' nodes in generating hybrid and multi-stable behaviors.

Findings

Discovery of new parameter regions with multi-stability.

Identification of hybrid motions in bimodal networks.

Demonstration of how 'mothership' nodes alter swarm dynamics.

Abstract

Swarming behavior continues to be a subject of immense interest because of its centrality in many naturally occurring systems in physics and biology, as well as its importance in applications such as robotics. Here we examine the effects on swarm pattern formation from delayed communication and topological heterogeneity, and in particular, the inclusion of a relatively small number of highly connected nodes, or "motherships", in a swarm's communication network. We find generalized forms of basic patterns for networks with general degree distributions, and a variety of new behaviors including new parameter regions with multi-stability and hybrid motions in bimodal networks. The latter is an interesting example of how heterogeneous networks can have dynamics that is a mix of different states in homogeneous networks, where high and low-degree nodes have simultaneously distinct behavior.