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dc.contributor.authorTsyganov, M. A.en_GB
dc.contributor.authorBrindley, J.en_GB
dc.contributor.authorHolden, A. V.en_GB
dc.contributor.authorBiktashev, V. N.en_GB
dc.date.accessioned2012-09-28T17:54:24Zen_GB
dc.date.accessioned2013-03-20T12:24:14Z
dc.date.issued2004en_GB
dc.description.abstractWe have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the ``taxis'', represented by nonlinear ``cross-diffusion'' terms in the mathematical formulation. We have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms, ``parabolic'' and ``linear''. Transition from one form to the other correlates with changes in the shape of the wave profile. Dependence of the propagation velocity on diffusion in this system differs from the square-root dependence typical of reaction-diffusion waves. We demonstrate also that, for systems with negative and positive taxis, for example, pursuit and evasion, there typically exists a large region in the parameter space, where the waves demonstrate quasisoliton interaction: colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries.en_GB
dc.identifier.citationVol. 197 (1–2), pp. 18–33en_GB
dc.identifier.doi10.1016/j.physd.2004.06.004en_GB
dc.identifier.urihttp://hdl.handle.net/10036/3766en_GB
dc.publisherElsevieren_GB
dc.relation.urlhttp://dx.doi.org/10.1016/j.physd.2004.06.004en_GB
dc.titleSoliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion exampleen_GB
dc.date.available2012-09-28T17:54:24Zen_GB
dc.date.available2013-03-20T12:24:14Z
dc.descriptionCopyright © 2004 Elsevieren_GB
dc.identifier.journalPhysica D: Nonlinear Phenomenaen_GB


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