Persistence in models of predator-prey populations with diffusion

DOI10.1016/0022-0396(86)90044-6zbMath0605.34044OpenAlexW1966264274MaRDI QIDQ1084252

Krzysztof P. Rybakowski, Klaus Schmitt, Steven R. Dunbar

Publication date: 1986

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(86)90044-6

zbMATH Keywords

diffusionpredator-prey systemsfirst order differential equation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Population dynamics (general) (92D25) Dynamical systems and ergodic theory (37-XX)

Related Items (20)

Uniform persistence in nonautonomous delay differential Kolmogorov-type population models ⋮ Uniform persistence and flows near a closed positively invariant set ⋮ Evolution of a semilinear parabolic system for migration and selection in population genetics ⋮ Permanence in ecological systems with spatial heterogeneity ⋮ Uniform persistence in reaction-diffusion plankton models ⋮ Robust permanence for ecological equations with internal and external feedbacks ⋮ Repellers in systems with infinite delay ⋮ Predator-prey models with almost periodic coefficients ⋮ Permanence in Kolmogorov periodic predator-prey models with diffusion ⋮ An almost periodic epidemic model in a patchy environment ⋮ Spreading speeds of a Lotka-Volterra predator-prey system: The role of the predator ⋮ A cohomological index of Conley type for multi-valued admissible flows ⋮ Persistence in population dynamics via local average liapunov functions ⋮ Persistence and spatial patterns in a one-predator-two-prey Lotka- Volterra model with diffusion ⋮ Permanence and the dynamics of biological systems ⋮ Permanence and global stability for cooperative Lotka-Volterra diffusion systems ⋮ Periodic solution and dynamical analysis for a delayed food chain model with general functional response and discontinuous harvesting ⋮ Global convergence of nonlinear cascade flows with Morse-Bott zero dynamics ⋮ Persistence of a class of periodic Kolmogorov systems ⋮ Global attractivity in monotone and subhomogeneous almost periodic systems

Cites Work

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• Persistence in models of three interacting predator-prey populations
• Persistence in a model of three competitive populations
• Large diffusivity and asymptotic behavior in parabolic systems
• Geometric theory of semilinear parabolic equations
• The Morse index, repeller-attractor pairs and the connection index for semiflows on noncompact spaces
• Differential equations and their applications. An introduction to applied mathematics
• Global stability in two species interactions
• Global stability in Lotka-Volterra systems with diffusion
• Local semi-dynamical systems

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