Torus bifurcations of large-scale swarms having range dependent communication delay

Dynamical emergent patterns of swarms are now fairly well established in nature, and include flocking and rotational states. Recently, there has been great interest in engineering and physics to create artificial self-propelled agents that communicate over a network and operate with simple rules, with the goal of creating emergent self-organizing swarm patterns. In this paper, we show that when communicating networks have range dependent delays, rotational states which are typically periodic, undergo a bifurcation and create swarm dynamics on a torus. The observed bifurcation yields additional frequencies into the dynamics, which may lead to quasi-periodic behavior of the swarm.Comment: 7 pages 8 figure

The chaotic milling behaviors of interacting swarms after collision

We consider the problem of characterizing the dynamics of interacting swarms after they collide and form a stationary center of mass. Modeling efforts have shown that the collision of near head-on interacting swarms can produce a variety of post-collision dynamics including coherent milling, coherent flocking, and scattering behaviors. In particular, recent analysis of the transient dynamics of two colliding swarms has revealed the existence of a critical transition whereby the collision results in a combined milling state about a stationary center of mass. In the present work we show that the collision dynamics of two swarms that form a milling state transitions from periodic to chaotic motion as a function of the repulsive force strength and its length scale. We used two existing methods as well as one new technique: Karhunen-Loeve decomposition to show the effective modal dimension chaos lives in, the 0-1 test to identify chaos, and then Constrained Correlation Embedding to show how each swarm is embedded in the other when both swarms combine to form a single milling state after collision. We expect our analysis to impact new swarm experiments which examine the interaction of multiple swarms

A Computer-Assisted Study of Red Coral Population Dynamics

We consider a 13-dimensional age-structured discrete red coral population model varying with respect to a fitness parameter. Our numerical results give a bifurcation diagram of both equilibria and stable invariant curves of orbits. We observe that not only for low levels of fitness, but also for high levels of fitness, populations are extremely vulnerable, in that they spend long time periods near extinction. We then use computer-assisted proofs techniques to rigorously validate the set of regular and bifurcation fixed points that have been found numerically.Comment: 31 pages, 12 figure