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Non‐Constant Positive Steady States of a Predator‐Prey System with Non‐Monotonic Functional Response and Diffusion
Author(s) -
Pang Peter Y. H.,
Wang Mingxin
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014321
Subject(s) - mathematics , functional response , monotonic function , constant (computer programming) , steady state (chemistry) , neumann boundary condition , diffusion , mathematical analysis , boundary (topology) , homogeneous , bifurcation , predation , predator , nonlinear system , thermodynamics , combinatorics , physics , paleontology , chemistry , computer science , biology , programming language , quantum mechanics
This paper deals with non‐constant positive steady‐state solutions of a predator‐prey system with non‐monotonic functional response, also called Holling type‐IV interaction terms, and diffusion under the homogeneous Neumann boundary condition. We first establish positive upper and lower bounds for such solutions, and then study their non‐existence, global existence and bifurcation. 2000 Mathematics Subject Classification 35J55, 92D25.