Global bifurcation in the Brusselator system
From MaRDI portal
Publication:4839283
DOI10.1016/0362-546X(94)00218-7zbMath0829.35010OpenAlexW2012394694MaRDI QIDQ4839283
Kenneth J. Brown, Fordyce A. Davidson
Publication date: 17 July 1995
Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0362-546x(94)00218-7
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)
Related Items (50)
Bifurcation and stability analysis of steady states to a Brusselator model ⋮ Random attractors of the stochastic extended Brusselator system with a multiplicative noise ⋮ A ratio-dependent predator-prey model with diffusion ⋮ Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion ⋮ Local and global bifurcation of steady states to a general Brusselator model ⋮ Spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law ⋮ Pattern formation in the Gray-Scott model ⋮ Qualitative analysis of a Belousov-Zhabotinskii reaction model ⋮ Turing-Hopf bifurcation analysis and normal form of a diffusive Brusselator model with gene expression time delay ⋮ Positive radial solutions for Dirichlet problem of quasilinear differential system with mean curvature operator in Minkowski space ⋮ Global dissipative dynamics of the extended Brusselator system ⋮ Non-constant positive steady states of a prey-predator system with cross-diffusions ⋮ On pattern formation in the Gray-Scott model ⋮ Bifurcation behaviors of steady-state solution to a discrete general Brusselator model ⋮ Hopf bifurcations in general systems of Brusselator type ⋮ Turing instability and Hopf bifurcation of a spatially discretized diffusive Brusselator model with zero-flux boundary conditions ⋮ Stationary patterns in a two-cell coupled isothermal chemical system with arbitrary powers of autocatalysis ⋮ Spatiotemporal patterns of a homogeneous diffusive predator-prey system with Holling type III functional response ⋮ Pattern formation in a general two-cell Brusselator model ⋮ Hopf bifurcation in general Brusselator system with diffusion ⋮ Global bifurcation analysis and pattern formation in homogeneous diffusive predator-prey systems ⋮ Coexistence of activator and inhibitor for Brusselator diffusion system in chemical or biochemical reactions ⋮ Hopf bifurcation and periodic solutions in a coupled Brusselator model of chemical reactions ⋮ Hopf Bifurcation and Self-Organization Pattern of a Modified Brusselator Model ⋮ High-Order Analysis of Canard Explosion in the Brusselator Equations ⋮ Stochastic bifurcation analysis in Brusselator system with white noise ⋮ SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL ⋮ Positive steady-state solutions of the Noyes--Field model for Belousov--Zhabotinskii reaction. ⋮ Influence of diffusion on the stability of a full Brusselator model ⋮ Stationary patterns caused by cross-diffusion for a three-species prey-predator model ⋮ Diffusion-driven instability and Hopf bifurcation in Brusselator system ⋮ Qualitative analysis for a biological depletion model ⋮ The stochastic Hopf bifurcation analysis in Brusselator system with random parameter ⋮ Pattern formation of a coupled two-cell Brusselator model ⋮ Bifurcation analysis of an enzyme-catalyzed reaction-diffusion system ⋮ TURING PATTERNS IN GENERAL REACTION-DIFFUSION SYSTEMS OF BRUSSELATOR TYPE ⋮ A priori bounds for reaction-diffusion systems arising in chemical and biological dynamics ⋮ Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues ⋮ Spatial pattern formation in activator-inhibitor models with nonlocal dispersal ⋮ \(L^2\)-energy stability via new dependent variables for circumventing strongly nonlinear reaction terms ⋮ Steady-State Bifurcation for a Biological Depletion Model ⋮ Non-constant positive steady states of the Sel'kov model. ⋮ Computer assisted proof of branches of stationary and periodic solutions, and Hopf bifurcations, for dissipative PDEs ⋮ On steady-state solutions of the Brusselator-type system ⋮ Non-constant stationary solutions to a prey-predator model with diffusion ⋮ Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay ⋮ Pattern formation in the Brusselator system ⋮ Nonconstant positive steady states for a ratio-dependent predator-prey system with cross-diffusion ⋮ An analytical studies of the reaction-diffusion systems of chemical reactions ⋮ Qualitative analysis of predator-prey models with Beddington-De Angelis functional response and diffusion
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- Brussellator Isolas
- Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations
- Analysis of bifurcations in reaction–diffusion systems with no-flux boundary conditions: the Sel'kov model
- Chaotic Wakes and Other Wave-Induced Behavior in a System of Reaction–Diffusion Equations
- Applications of functional analysis and operator theory
This page was built for publication: Global bifurcation in the Brusselator system