Quasisoliton interaction of pursuit-evasion waves in a predator-prey system

We consider a system of partial differential equations describing two spatially distributed populations in a "predator-prey" interaction with each other. The spatial evolution is governed by three processes: positive taxis of predators up the gradient of prey (pursuit), negative taxis of p...

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Bibliographic Details
Published in:Physical review letters 2003-11, Vol.91 (21), p.218102-218102, Article 218102
Main Authors: Tsyganov, M A, Brindley, J, Holden, A V, Biktashev, V N
Format: Article
Language:English
Subjects:
Animals
Models, Biological
Population Dynamics
Predatory Behavior
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Summary:We consider a system of partial differential equations describing two spatially distributed populations in a "predator-prey" interaction with each other. The spatial evolution is governed by three processes: positive taxis of predators up the gradient of prey (pursuit), negative taxis of prey down the gradient of predators (evasion), and diffusion resulting from random motion of both species. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the taxis and is entirely different from waves in a reaction-diffusion system. Unlike typical reaction-diffusion waves, which annihilate on collision, these "taxis" waves can often penetrate through each other and reflect from impermeable boundaries.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.91.218102