A minimal model of predator–swarm interactions
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 ‘weak’ predator, the swarm is able to escape the predator completely. As the strength is increased, th...
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| Published in | Journal of the Royal Society interface Vol. 11; no. 94; p. 20131208 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
England
The Royal Society
06.05.2014
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| Subjects | |
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| Abstract | 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 ‘weak’ 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 is able to escape by ‘confusing’ the predator: the prey forms a ring with the predator at the centre. 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 (owing 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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| AbstractList | 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 'weak' 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 is able to escape by 'confusing' the predator: the prey forms a ring with the predator at the centre. 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 (owing 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. |
| Author | Kolokolnikov, Theodore Chen, Yuxin |
| AuthorAffiliation | 2 Department of Mathematics and Statistics , Dalhousie University , Halifax , Canada 1 Department of Engineering Sciences and Applied Mathematics , Northwestern University , Evanston, IL , USA |
| AuthorAffiliation_xml | – name: 2 Department of Mathematics and Statistics , Dalhousie University , Halifax , Canada – name: 1 Department of Engineering Sciences and Applied Mathematics , Northwestern University , Evanston, IL , USA |
| Author_xml | – sequence: 1 givenname: Yuxin surname: Chen fullname: Chen, Yuxin organization: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, USA – sequence: 2 givenname: Theodore surname: Kolokolnikov fullname: Kolokolnikov, Theodore email: tkolokol@gmail.com organization: Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/24598204$$D View this record in MEDLINE/PubMed |
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| Snippet | We propose a minimal model of predator–swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed... We propose a minimal model of predator-swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed... |
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| SubjectTerms | Animals Biological Aggregation Cooperative Behavior Dynamical Systems Models, Biological Predatory Behavior - physiology Predator–prey Interactions |
| Title | A minimal model of predator–swarm interactions |
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