# Stable Swarming Using Adaptive Long-range Interactions

## TL;DR

This paper investigates how adaptive, energy-consuming sensory mechanisms influence long-range attractive interactions in biological swarms, revealing that adaptivity prevents collapse and promotes self-stability in both 2D and 3D systems.

## Contribution

It introduces a model of adaptive long-range interactions in swarms and demonstrates their stabilizing effect against collapse through linear stability analysis.

## Key findings

- Adaptive forces decrease or stay constant with increasing swarm density.
- Adaptivity prevents collapse (Jeans instability) in swarm models.
- Self-stabilization emerges naturally from adaptive interactions.

## Abstract

Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the response produced by the sensor is adapted to the overall amplitude of the signal; reducing the sensitivity in the presence of strong stimulus, while increasing it when it is weak. This property is inherently energy consuming and a manifestation of the non-equilibrium nature of living organisms. We explore here how adaptivity affects the effective forces that organisms feel due to others in the context of a uniform swarm, both in two and three dimensions. The interactions between the individuals are taken to be attractive and long-range, of power-law form. We find that the effects of adaptivity inside the swarm are dramatic, where the effective forces decrease (or remain constant) with increasing swarm density. Linear stability analysis demonstrates how this property prevents collapse (Jeans instability), when the forces are adaptive. Adaptivity therefore endows swarms with a natural mechanism for self-stabilization.