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Painlevé analysis and exact solutions of a predator–prey system with diffusion
Author(s) -
Kudryashov N.A.,
Zakharchenko A.S.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3156
Subject(s) - mathematics , predation , logistic function , diffusion , traveling wave , predator , function (biology) , mathematical analysis , statistics , ecology , thermodynamics , physics , biology , evolutionary biology
A system of equations for description of the predator–prey relations is considered. The model corresponds to the modified Lotka–Volterra system with logistic growth of the prey and with both predator and prey dispersing by diffusion. The Painlevé analysis of the system of equations is studied. Exact traveling wave solutions are found by means of the Q ‐function method. Copyright © 2014 John Wiley & Sons, Ltd.