Spatial Models of Bistability in Biological Collectives

Derek A. Paley, Naomi Ehrich Leonard, Rodolphe J. Sepulchre and Iain D. Couzin

Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, December 2007.
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 selfpropelled particles with coupled-oscillator dynamics.

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