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Papers on the Brusselator – early and recent

Model G is based on the Brusselator adding an extra G component. To understand Model G better we need to look at the Brusselator and how it was derived. See these papers below. N.B. sorry I can’t upload them to this site at the moment. Working on it. Brendan

Paper 1:

BULLETIN OF MATHEMATICAL BIOLOGY VOLUME 37 1975

BIFURCATION ANALYSIS OF NONLINEAR REACTION – DIFFUSION EQUATIONS–I. EVOLUTION EQUATIONS AND THE STEADY STATE SOLUTIONS

J. F. G. Auchmuty
Department of Mathematics,
Indiana University,
Bloomington, Indiana 47401
and
G. Nicolis
Faculty des Sciences,
Universite Libre de Bruxelles,
Belgium

https://www.researchgate.net/publication/242968205_Bifurcation_analysis_of_nonlinear_reaction-diffusion_equations-I_Evolution_equations_and_the_steady_state_solutions

Paper 2

BULLETIN OF MATHEMATICAL BIOLOGY VOLUME 37 1975

BIFURCATION ANALYSIS OF NONLINEAR REACTION-DIFFUSION EQUATIONS–II. STEADY STATE SOLUTIONS AND COMPARISON WITH NUMERICAL SIMULATIONS

M. Herschkowitz-Kaufman
Faeulte des Sciences,
Universite Libre de Bruxelles
Belgium

Paper 3

CHAOS 27, 104617 (2017)

Dissipative structures: From reaction-diffusion to chemo-hydrodynamic patterns

M. A. Budroni and A. De Wit

Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Theorique,
Universite libre de Bruxelles (ULB), CP 231 – Campus Plaine, 1050 Brussels, Belgium

https://nlpc.ulb.be/pdf/17.Budroni_CHAOS_Prigogine.pdf

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Simulating Model G neutral 3D particle in 1D with a G gradients -1/80 to -1/10

Video 1: Simulating Model G neutral 3D particle in 1D with a G gradient – using Mathematica. Gradient = -1/80.

See code here @ https://github.com/bjdarrer/Model_G_Particle_3D_in_1D_gradient_-1By80_1a/blob/main/Model_G_Particle_3D_in_1D_gradient_-1By80_1a.nb

Video 2: Simulating Model G neutral 3D particle in 1D with a G gradient – using Mathematica. Gradient = -1/50.

Video 3: Simulating Model G neutral 3D particle in 1D with a G gradient – using Mathematica. Gradient = -1/30.

Video 4: Simulating Model G neutral 3D particle in 1D with a G gradient – using Mathematica. Gradient = -1/20.

Video 5: Simulating Model G neutral 3D particle in 1D with a G gradient – using Mathematica. Gradient = -1/10.

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Simulating Model G neutral particle in a G gradient with Mathematica

Video 1: “particle in gradient slope80 bjd 1e” — Simulating Model G neutral particle in a G gradient with Mathematica. Gradient = -1/80

Video 2: “particle in gradient slope50 bjd 1c” — Simulating Model G neutral particle in a G gradient with Mathematica. Gradient = -1/50

Video 3: “particle in gradient slope30 bjd 1h” — Simulating Model G neutral particle in a G gradient with Mathematica. Gradient = -1/30

Video 4: “particle in gradient slope20 bjd 1f” — Simulating Model G neutral particle in a G gradient with Mathematica. Gradient = -1/20

Video 5: “particle in gradient slope10 bjd 1g” — Simulating Model G neutral particle in a G gradient with Mathematica. Gradient = -1/10