On the global asymptotic stability of solutions to a generalised Lengyel-Epstein system

DOI10.1016/j.nonrwa.2016.11.007zbMath1367.35085OpenAlexW2566868778MaRDI QIDQ505236

Samir Bendoukha, Salem Abdelmalek

Publication date: 19 January 2017

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2016.11.007

zbMATH Keywords

Lyapunov functionalreaction-diffusion equationsglobal asymptotical stabilityLengyel-Epstein system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (13)

Numerical study and stability of the Lengyel-Epstein chemical model with diffusion ⋮ Analysis on a generalized Sel'kov-Schnakenberg reaction-diffusion system ⋮ Bifurcations and pattern formation in a generalized Lengyel-Epstein reaction-diffusion model ⋮ Asymptotic stability of solutions for a diffusive epidemic model ⋮ Global and local asymptotic stability of an epidemic reaction‐diffusion model with a nonlinear incidence ⋮ Extended global asymptotic stability conditions for a generalized reaction-diffusion system ⋮ On the asymptotic stability of the time-fractional Lengyel-Epstein system ⋮ Persistence and Turing instability in a cross-diffusive predator-prey system with generalist predator ⋮ Pattern formation of a biomass-water reaction-diffusion model ⋮ The global existence and asymptotic stability of solutions for a reaction-diffusion system ⋮ Bifurcations in Twinkling Patterns for the Lengyel–Epstein Reaction–Diffusion Model ⋮ Hopf and Bautin bifurcations in a generalized Lengyel-Epstein system ⋮ The Lengyel–Epstein Reaction Diffusion System

Uses Software

• Matlab

Cites Work

• On the global dynamics of the Lengyel-Epstein system
• Diffusion-driven instability and bifurcation in the Lengyel-Epstein system
• Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system
• Diffusion, self-diffusion and cross-diffusion
• Hopf bifurcation and Turing instability of 2-D Lengyel-Epstein system with reaction-diffusion terms
• Convergence to Homogeneous Equilibrium State for Generalized Volterra–Lotka Systems with Diffusion
• A chemical approach to designing Turing patterns in reaction-diffusion systems.
• Stability Properties of Solutions to Systems of Reaction-Diffusion Equations
• The chemical basis of morphogenesis
• Turing patterns in the Lengyel-Epstein system for the CIMA reaction

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