brusselator model  (Informa UK Limited)

Journal: BMC Systems Biology

Article Title: Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

doi: 10.1186/1752-0509-8-45

Figure Lengend Snippet: SIMULINK construction of the Brusselator model.

Article Snippet: Assuming h ≡ h x = h y (i.e., a square grid), the discrete Laplacian operation in a one-dimensional Cartesian coordinates along the y -axis has the form: (9) ∇ 1D 2 U i , j ≈ U i , j + 1 - 2 U i , j + U i , j - 1 h 2 ; for the two-dimensional case, we have (10) ∇ 2D 2 U i , j ≈ U i + 1 , j + U i - 1 , j - 4 U i , j + U i , j + 1 + U i , j - 1 h 2 In SIMULINK , we initialise the Brusselator model as a column vector consisting of a 60 × 1 grid (spatial resolution = 1 cm/grid-point) for the one-dimensional case; or as a 60 × 60 grid for the two-dimensional case.

Techniques:

Journal: BMC Systems Biology

Article Title: Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

doi: 10.1186/1752-0509-8-45

Figure Lengend Snippet: Brusselator simulation in 1-D space. Left column: dispersion curve of real ( α ) and imaginary ( ω ) parts of dominnat eigenvalues predicting the emergent pattens for two sets of parameters: (a) A = 2.5, B = 9, D X = 7, D Y = 10; (b) A = 2, B = 4.8, D X = 2, D Y = 10. H: Hopf mode with α > 0, ω > 0 at wavenumber q = 0; T: Turing mode with α > 0, ω = 0 at q ≠ 0; DT: damped Turing with α < 0 at q ≠ 0; DH: damped Hopf with α < 0 at q = 0. Right column: one-dimensional Brusselator model of length 60 cm with periodic boundary condition evolves in time running rightwards during 30 s. Colour indicates the local concentration of the reactant: [red] high concentration, [blue] low concentration.

Article Snippet: Assuming h ≡ h x = h y (i.e., a square grid), the discrete Laplacian operation in a one-dimensional Cartesian coordinates along the y -axis has the form: (9) ∇ 1D 2 U i , j ≈ U i , j + 1 - 2 U i , j + U i , j - 1 h 2 ; for the two-dimensional case, we have (10) ∇ 2D 2 U i , j ≈ U i + 1 , j + U i - 1 , j - 4 U i , j + U i , j + 1 + U i , j - 1 h 2 In SIMULINK , we initialise the Brusselator model as a column vector consisting of a 60 × 1 grid (spatial resolution = 1 cm/grid-point) for the one-dimensional case; or as a 60 × 60 grid for the two-dimensional case.

Techniques: Dispersion, Concentration Assay

Journal: BMC Systems Biology

Article Title: Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

doi: 10.1186/1752-0509-8-45

Figure Lengend Snippet: Turing mode stability of the Brusselator model in 2-D space. Each coloured stability curve represents specific mode: red = Stripes, blue = H 0 , black = H π . Solid and dashed curves correspond to stable and unstable modes respectively, according to mode stability analysis. Five representative μ values are selected for comparison of theoretical predictions for mode stability against practical simulations (shown as subplots). Colour of the pattern indicates the local concentration of the reactant: [red] high concentration, [blue] low concentration. Model parameters: A = 5, D X = 5, D Y = 40.

Article Snippet: Assuming h ≡ h x = h y (i.e., a square grid), the discrete Laplacian operation in a one-dimensional Cartesian coordinates along the y -axis has the form: (9) ∇ 1D 2 U i , j ≈ U i , j + 1 - 2 U i , j + U i , j - 1 h 2 ; for the two-dimensional case, we have (10) ∇ 2D 2 U i , j ≈ U i + 1 , j + U i - 1 , j - 4 U i , j + U i , j + 1 + U i , j - 1 h 2 In SIMULINK , we initialise the Brusselator model as a column vector consisting of a 60 × 1 grid (spatial resolution = 1 cm/grid-point) for the one-dimensional case; or as a 60 × 60 grid for the two-dimensional case.

Techniques: Comparison, Concentration Assay