| Contents |
| We propose a minimal model of predator-swarm interactions which captures many
of the essential dynamics observed in nature. Different outcomes are observed
depending on the predator strength. For a \textquotedblleft
weak\textquotedblright\ predator, the swarm is able to escape the predator
completely. As the strength is increased, the predator is able to catch up
with the swarm as a whole, but the individual prey are able to escape by
\textquotedblleft confusing\textquotedblright\ the predator:\ the prey forms a
ring with the predator at the center. For higher predator strength, complex
chasing dynamics are observed which can become chaotic. For even higher
strength, the predator is able to successfully capture the prey. Our model is
simple enough to be amenable to a full mathematical analysis which is used to
predict the shape of the swarm as well as the resulting predator-prey dynamics
as a function of model parameters. We show that as the predator strength is
increased, there is a transition (due to a Hopf bifurcation)\ from confusion
state to chasing dynamics, and we compute the threshold analytically. Our
analysis indicates that the swarming behaviour is not helpful in avoiding the
predator, suggesting that there are other reasons why the species may swarm.
The complex shape of the swarm in our model during the chasing dynamics is
similar to the shape of a flock of sheep avoiding a shepherd. |
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