Note on the Lyapunov functional method

DOI10.1016/j.aml.2017.07.003OpenAlexW2736745096MaRDI QIDQ1680788

Mingxin Wang

Publication date: 16 November 2017

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

Full work available at URL: https://doi.org/10.1016/j.aml.2017.07.003

zbMATH Keywords

global stabilityLyapunov functional methodreaction diffusion systems

Mathematics Subject Classification ID

Related Items (18)

Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion ⋮ Global existence and asymptotic behavior of solutions for some coupled systems via a Lyapunov functional ⋮ Bistability and Turing pattern induced by cross fraction diffusion in a predator-prey model ⋮ Global stability of nonhomogeneous steady-state solution in a Lotka-Volterra competition-diffusion-advection model ⋮ On a Lotka-Volterra competition-diffusion-advection model in general heterogeneous environments ⋮ An analytical approach to determining the coefficients in Lyapunov direct method: with application to an age-structured epidemiological model ⋮ Dynamics of consumer-resource reaction-diffusion models: single and multiple consumer species ⋮ A diffusive SIS epidemic model with saturated incidence function in a heterogeneous environment ^* ⋮ Global stability of nonhomogeneous coexisting equilibrium state for the multispecies Lotka–Volterra mutualism models with diffusion ⋮ The dynamics of an eco-epidemiological prey-predator model with infectious diseases in prey ⋮ Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model ⋮ The stability of equilibria for a reaction-diffusion-ODE system on convex domains ⋮ Boundedness and global stability of a diffusive prey–predator model with prey-taxis ⋮ Global existence and asymptotic stability for a class of coupled reaction-diffusion systems on growing domains ⋮ Global $L^\infty$-bounds and Long-time Behavior of a Diffusive Epidemic System in A Heterogeneous Environment ⋮ The dynamics of a predator-prey model with diffusion and indirect prey-taxis ⋮ Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model ⋮ Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

Cites Work

• A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment
• Uniform bounds from bounded \(L_ p-\)functionals in reaction-diffusion equations
• Strategy and stationary pattern in a three-species predator--prey model

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