Georgia Institute of Technology College of Sciences

The study of collective behavior---of animals, mechanical systems, or even abstract oscillators---has fascinated a large number of researchers from observational geologists to pure mathematicians. We consider the collective behavior of herds of cattle. We first consider some results from an agent-based model and then formulate a mathematical model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds, finding that it is possible for cows to synchronize less when the coupling is increased. [This research is in collaboration with Jie Sun, Erik Bollt, and Marian Dawkins.]