A sufficient and necessary condition for the existence of positive solutions for a prey-predator system with Ivlev-type functional response

DOI10.1016/J.AML.2011.01.027zbMath1216.35158OpenAlexW2019843907WikidataQ115598033 ScholiaQ115598033MaRDI QIDQ533448

Yunfeng Jia

Publication date: 3 May 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.01.027

zbMATH Keywords

positive solutionfixed point indexpredator-prey modelIvlev-type functional response

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Applications of operator theory to differential and integral equations (47N20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Second-order elliptic systems (35J47) Positive solutions to PDEs (35B09) Boundary value problems for second-order elliptic systems (35J57)

Related Items (5)

Effects of the self- and cross-diffusion on positive steady states for a generalized predator-prey system ⋮ Qualitative analysis on a predator-prey model with Ivlev functional response ⋮ Existence, multiplicity, and stability of positive solutions of a predator-prey model with dinosaur functional response ⋮ Non-constant positive solutions of a general Gause-type predator-prey system with self- and cross-diffusions ⋮ Stability and bifurcation in a stage-structured predator–prey system with Holling-II functional response and multiple delays

Cites Work

• Dynamics of a Ivlev-type predator-prey system with constant rate harvesting
• Permanence and stability of an Ivlev-type predator-prey system with impulsive control strategies
• Two-parameter bifurcation in a predator-prey system of Ivlev type
• The dynamics of a predator-prey model with Ivlev's functional response concerning integrated pest management
• On positive solutions of a nonlinear equilibrium boundary value problem
• On the indices of fixed points of mappings in cones and applications
• Dynamics of a class of nonautonomous semi-ratio-dependent predator--prey systems with functional responses
• A predator-prey model with Ivlev's functional response
• On Positive Solutions of Some Pairs of Differential Equations
• Coexistence Theorems of Steady States for Predator-Prey Interacting Systems
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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