Asymptotic behaviour of solutions of periodic competition diffusion system

DOI10.1016/0362-546X(89)90054-0zbMath0686.35060MaRDI QIDQ4204530

Shair Ahmad, Alan C. Lazer

Publication date: 1989

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

uniquenessNeumann boundary conditionExistence

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Maximum principles in context of PDEs (35B50)

Related Items (56)

Quasisolutions and dynamics of time-periodic nonquasimonotone reaction-diffusion systems ⋮ Permanence and asymptotic stability for competitive and Lotka-Volterra systems with diffusion. ⋮ Existence of a global coexistence state for periodic competition diffusion systems ⋮ Periodic optimal control for competing parabolic Volterra-Lotka-type systems ⋮ On an abstract competition model and applications ⋮ Global existence and asymptotic behavior of solutions to a predator-prey chemotaxis system with two chemicals ⋮ Asymptotic behavior of solutions of a periodic reaction-diffusion system of a three-species of competition model ⋮ On the periodic Lotka-Volterra competition model ⋮ Asymptotic periodicity and permanence in a competition-diffusion system with discrete delays ⋮ \({\mathcal A}\)-stability of global attractors of competition diffusion systems ⋮ Protection zones in periodic-parabolic problems ⋮ Diffusion-induced extinction of a superior species in a competition system ⋮ Coexistence Solutions for a Periodic Competition Model with Singular–Degenerate Diffusion ⋮ Coupled non-local periodic parabolic systems with time delays ⋮ On positive solutions of the Lotka--Volterra cooperating models with diffusion ⋮ Existence of global coexistence state for periodic competition diffusion systems ⋮ Population systems with nonlinear discrete diffusion terms. ⋮ On positive periodic solutions of the time-space periodic Lotka-Volterra cooperating system in multi-dimensional media ⋮ Asymptotic periodicity in diffusive logistic equations with discrete delays ⋮ Asymptotic bounds of solutions for a periodic doubly degenerate parabolic equation ⋮ Asymptotic behavior of the principal eigenvalue for cooperative periodic-parabolic systems and applications ⋮ A sufficient condition for the existence of periodic solution for a reaction diffusion equation with infinite delay. ⋮ Conditions for permanence in well-known biological competition models ⋮ Practical persistence in ecological models via comparison methods ⋮ Continuous and discrete periodic asymptotic behavior of solutions to a competitive chemotaxis PDEs system ⋮ Diffusive Holling-Tanner predator-prey models in periodic environments ⋮ Effect of domain-shape on coexistence problems in a competition-diffusion system ⋮ Periodic solution and oscillation in a competition model with diffusion and distributed delay effects ⋮ Existence and stability of periodic solutions for parabolic systems with time delays ⋮ Permanence and asymptotic stability in diagonally convex reaction–diffusion systems ⋮ Asymptotic behavior of periodic competition diffusion system ⋮ Coexistence and extinction in time-periodic Volterra-Lotka type systems with nonlocal dispersal ⋮ Asymptotic behavior of solutions of a periodic diffusion equation ⋮ Positive periodic solutions of a Hassell-Varley type predator-prey system ⋮ Periodic solutions of a class of degenerate parabolic system with delays ⋮ A two-species cooperative Lotka-Volterra system of degenerate parabolic equations ⋮ The existence, uniqueness and stability of positive periodic solution for periodic reaction-diffusion system. ⋮ Periodic solutions for the degenerate Lotka-Volterra competition system ⋮ Asymptotic behavior of solutions of a periodic diffusion system of plankton allelopathy ⋮ Periodic solutions of quasilinear parabolic systems with nonlinear boundary conditions ⋮ Stability and attractivity of periodic solutions of parabolic systems with time delays ⋮ Asymptotic behavior of solutions of a periodic diffusion system ⋮ Convergence in almost periodic competition diffusion systems ⋮ Persistence in a periodic competitor-competitor-mutualist diffusion system ⋮ Classification of global dynamics of competition models with nonlocal dispersals. I: Symmetric kernels ⋮ Diffusive Lotka-Volterra competition models on periodically evolving domains ⋮ On the Nonautonomous Volterra-Lotka Competition Equations ⋮ Time periodic solutions of a class of degenerate parabolic equations ⋮ Global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model ⋮ Periodic solutions of systems of parabolic equations in unbounded domains ⋮ Cyclic competition of three species in the time periodic and diffusive case ⋮ Global existence and asymptotic behavior of solutions to a chemotaxis system with chemicals and prey-predator terms ⋮ Periodic solutions of parabolic systems with nonlinear boundary conditions ⋮ Existence and stability of periodic quasisolutions in nonlinear parabolic systems with discrete delays ⋮ Periodic solutions of parabolic systems with time delays ⋮ Discrete infinite-dimensional type-\(K\) monotone dynamical systems and time-periodic reaction--diffusion systems.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence and ultimate bounds of solutions of the nonautonomous Volterra-Lotka competition equations
• Bifurcation of periodic solutions of periodic evolution equations in a cone
• Coexistence and stability of a competition-diffusion system in population dynamics
• An application of topological degree to the periodic competing species problem
• Asymptotic behavior of a competition—diffusion system in population dynamics
• Stable Coexistence States in the Volterra–Lotka Competition Model with Diffusion
• Exchange of equilibria in two species Lotka-Volterra competition models
• Decay to Uniform States in Ecological Interactions

This page was built for publication: Asymptotic behaviour of solutions of periodic competition diffusion system