Adversarial Swarms as Dynamical Systems

TL;DR

This study models adversarial swarms as dynamical systems, revealing complex chaotic behaviors and the 'edge of chaos' phenomenon through simulations, Lyapunov exponents, and entropy analysis.

Contribution

It introduces an agent-based adversarial swarm model analyzed from a dynamical systems perspective, highlighting chaos and complexity in swarm interactions.

Findings

Chaotic behavior predominantly observed in Defenders

Presence of multiple local equilibrium points

Defenders exhibit higher randomness than Attackers

Abstract

An Adversarial Swarm model consists of two swarms that are interacting with each other in a competing manner. In the present study, an agent-based Adversarial swarm model is developed comprising of two competing swarms, the Attackers and the Defenders, respectively. The Defender's aim is to protect a point of interest in unbounded 2D Euclidean space referred to as the Goal. In contrast, the Attacker's main task is to intercept the Goal while continually trying to evade the Defenders, which gets attracted to it when they are in a certain vicinity of the Goal termed as the sphere of influence, essentially a circular perimeter. The interaction of the two swarms was studied from a Dynamical systems perspective by changing the number of Agents making up each respective swarm. The simulations were strongly investigated for the presence of chaos by evaluating the Largest Lyapunov Exponent (LLE), implementing phase space reconstruction. The source of chaos in the system was observed to be induced by the passively constrained motion of the Defender agents around the Goal. Multiple local equilibrium points existed for the Defenders in all the cases and some instances for the Attackers, indicating complex dynamics. LLEs for all the trials of the Monte Carlo analysis in all the cases revealed the presence of chaotic and non-chaotic solutions in each case, respectively, with the majority of the Defenders indicating chaotic behavior. Overall, the swarms exist in the 'Edge of chaos', thus revealing complex dynamical behavior. The final system state (i,e, the outcome of the interaction between the swarms in a particular simulation) is studied for all the cases, which indicated the presence of binary final states in some. Finally, to evaluate the complexity of individual swarms, Multiscale Entropy is employed, which revealed a greater degree of randomness for the Defenders when compared to Attackers.