Coherent Pattern Prediction in Swarms of Delay-Coupled Agents

Abstract

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatiotemporal scales of the swarm structures, as well as demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.

Hybrid dynamics in delay-coupled swarms with mothership networks

“…This typically leads to coherent rotation, known as the rotating state, which is shown in Fig.1(d). Together the three states comprise the known dynamical modes for swarming networks with delay [11,12]. Phase diagrams are shown in Fig.2 for bimodal networks.…”

“…Several recent works in swarm pattern formation have focused on time-delay effects, which can produce new patterns and bistability [11][12][13]. Delays model the finite time required for agents to send and process information in real systems.…”

“…For simplicity and analytic tractability, we assume that the mutual forces are springlike: ∇ r i U (r i (t) − r j (t − τ )) = r i (t) − r j (t − τ ), though sufficiently small repulsive terms do not alter the dynamics [11].…”

Collective Motions of Heterogeneous Swarms

“…This simplified model does not include short-range repulsion or other collision-avoidance strategies; however, earlier studies with homogeneous swarms indicate that the collective dynamics of the swarm are not significantly altered by the introduction of short-range repulsion terms [1].…”

“…We extend the model in [1] to the case where the swarm is divided into two distinct populations with different motion capabilities. The inspiration for our model comes from the idea of using swarms of autonomous mobile agents as sensor platforms to survey/monitor an area of interest.…”