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Positive solutions for ratio-dependent predator-prey interaction systems. (English) Zbl 1330.35478
Summary: We study the dynamics of predator-prey interaction systems between two species with ratio-dependent functional responses. First we provide sufficient and necessary conditions for positive steady-state solutions, and then we investigate the relationships between positive equilibria and positive solutions of the system over a large domain. Furthermore, we deal with the uniqueness and the stability of positive steady-states solutions with some assumptions. In addition, we discuss the extinction and the persistence results of time-dependent positive solutions to the system.

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
47N20 Applications of operator theory to differential and integral equations
92D25 Population dynamics (general)
Full Text: DOI
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