2007-12, Paley, Derek A., Ehrich Leonard, Naomi, Sepulchre, Rodolphe, Couzin, Iain D.

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion under slow variation of the neighborhood size in which individuals tend to align with one another. In the case that the neighborhood radius is less than the circular motion radius, both circular and parallel motion can occur. We provide Lyapunov-based analysis of bistability of circular and parallel motion in a closed-loop system of self-propelled particles with coupled-oscillator dynamics.

2007-12, Swain, Daniel T., Ehrich Leonard, Naomi, Couzin, Iain D., Kao, Albert B., Sepulchre, Rodolphe J.

Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns being towards the front, sides and back of the group. We propose a model and control laws to investigate the connections between these spatial dynamics, communication when sensing is range or direction limited, and convergence of coordinated group motions.