Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model

DOI10.1016/j.jmaa.2010.02.002zbMath1191.35043OpenAlexW2052727578MaRDI QIDQ961043

Linglong Du, Mingxin Wang

Publication date: 29 March 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.02.002

zbMATH Keywords

Hopf bifurcationNeumann problemLengyel-Epstein modelnon-homogeneous periodic solutions

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (29)

Spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law ⋮ Hopf bifurcation in spatially homogeneous and inhomogeneous autocatalysis models ⋮ Hopf bifurcation in a reaction-diffusion model with Degn-Harrison reaction scheme ⋮ Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack ⋮ Spatiotemporal patterns and bifurcations with degeneration in a symmetry glycolysis model ⋮ Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model ⋮ Bifurcation and spatiotemporal patterns of a density-dependent predator–prey model with Crowley–Martin functional response ⋮ Turing instability and pattern formation for the Lengyel-Epstein system with nonlinear diffusion ⋮ Dynamics of nonconstant steady states of the Sel'kov model with saturation effect ⋮ Stability and Hopf bifurcation in the general Langford system ⋮ Hopf bifurcation and steady-state bifurcation for an autocatalysis reaction-diffusion model ⋮ Turing Patterns in the Lengyel–Epstein System with Superdiffusion ⋮ Qualitative analysis on positive steady-state solutions for an autocatalysis model with high order ⋮ Turing-Hopf bifurcation in the reaction-diffusion equations and its applications ⋮ Bifurcation solutions in the diffusive minimal sediment ⋮ Hopf bifurcation and Turing instability of 2-D Lengyel-Epstein system with reaction-diffusion terms ⋮ Hopf bifurcations in Lengyel-Epstein reaction-diffusion model with discrete time delay ⋮ Hopf bifurcation and steady-state bifurcation for a Leslie-Gower prey-predator model with strong allee effect in prey ⋮ Steady-state bifurcation and Hopf bifurcation for a diffusive Leslie-Gower predator-prey model ⋮ Turing-Hopf bifurcation and multi-stable spatio-temporal patterns in the Lengyel-Epstein system ⋮ Bifurcation analysis of a diffusive predator-prey system with nonconstant death rate and Holling III functional response ⋮ Spatiotemporal patterns in the lengyel-Epstein reaction-diffusion model ⋮ Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response ⋮ Delay Effects on the Dynamics of the Lengyel–Epstein Reaction-Diffusion Model ⋮ Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay ⋮ Dynamics analysis of a chemical reaction-diffusion model subject to Degn-Harrison reaction scheme ⋮ Bifurcations in a diffusive predator–prey model with predator saturation and competition response ⋮ TURING-HOPF BIFURCATION IN THE REACTION-DIFFUSION SYSTEM WITH DELAY AND APPLICATION TO A DIFFUSIVE PREDATOR-PREY MODEL ⋮ Hopf bifurcations of a Lengyel-Epstein model involving two discrete time delays

Cites Work

• Unnamed Item
• Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
• Diffusion-driven instability and bifurcation in the Lengyel-Epstein system
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
• Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system
• Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model
• Turing patterns in the Lengyel-Epstein system for the CIMA reaction

This page was built for publication: Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model