期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 197, 期 1-2, 页码 18-33出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2004.06.004
关键词
population taxis waves; population dynamics; wave-splitting
We have studied properties of non-linear 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 non-linear 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 also demonstrate 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 quasi-soliton interaction; colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries. (C) 2004 Elsevier B.V. All rights reserved.
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