File:Bruesselator.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 744 × 580 pixels. Other resolutions: 308 × 240 pixels | 616 × 480 pixels | 985 × 768 pixels | 1,280 × 998 pixels | 2,560 × 1,996 pixels.
Original file (SVG file, nominally 744 × 580 pixels, file size: 233 KB)
File information
Structured data
Captions
Contents
Summary[edit]
DescriptionBruesselator.svg |
English: solution of "brusselator" differential equations for different conditions |
Date | |
Source | Own work |
Author | Jkrieger |
Other versions | File:bruesselator_de.svg |
Source Code[edit]
Source code
InfoField
MATLAB code
function bruesselator_time()
clear;
% timestep
DeltaT=0.1;
% reaction constants
k1=1;
k2=1;
k3=1;
k4=1;
% initial concentrations
X0=1;
Y0=1;
% constant concentrations
A=1;
B=3;
figure(1)
subplot(2,2,1)
options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);
f=@(t,y) bruesselator(t,y,k1,k2,k3,k4,A,B);
[T,Y] = ode45(f,[0 30],[X0 Y0],options);
plot (T,Y(:,1),'r-', 'LineWidth',2)
hold on
plot(T,Y(:,2),'b-', 'LineWidth',2)
hold off
xlabel('time [A.U.]');
ylabel('concentration [A.U.]');
legend('species X', 'species Y');
title('solution of bruesselator for X_0=Y_0=1, A=1, B=3, k_i=1 \forall i');
subplot(2,2,2)
[T,Y] = ode45(f,[0 200],[1 1],options);
[T,Y1] = ode45(f,[0 200],[1.5 3],options);
[T,Y2] = ode45(f,[0 200],[3 4],options);
plot(Y1(:,1),Y1(:,2), 'b-');
hold on
plot(Y2(:,1),Y2(:,2), 'k-');
plot(Y(:,1),Y(:,2), 'r-');
hold off
legend('X_0=1.5, Y_0=3', 'X_0=3, Y_0=4', 'X_0=1, Y_0=1')
xlabel('concentration X [A.U.]');
ylabel('concentration Y [A.U.]');
title('phase space plot for X_0=Y_0=1, A=1, B=3, k_i=1 \forall i');
A=1;
B=1.7;
subplot(2,2,3)
options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);
f=@(t,y) bruesselator(t,y,k1,k2,k3,k4,A,B);
[T,Y] = ode45(f,[0 30],[X0 Y0],options);
plot (T,Y(:,1),'r-', 'LineWidth',2)
hold on
plot(T,Y(:,2),'b-', 'LineWidth',2)
hold off
xlabel('time [A.U.]');
ylabel('concentration [A.U.]');
legend('species X', 'species Y');
title('solution of bruesselator for X_0=Y_0=1, A=1, B=1.7, k_i=1 \forall i');
subplot(2,2,4)
[T,Y] = ode45(f,[0 200],[1 1],options);
[T,Y1] = ode45(f,[0 200],[1.5 3],options);
[T,Y2] = ode45(f,[0 200],[3 4],options);
plot(Y1(:,1),Y1(:,2), 'b-');
hold on
plot(Y2(:,1),Y2(:,2), 'k-');
plot(Y(:,1),Y(:,2), 'r-');
hold off
legend('X_0=1.5, Y_0=3', 'X_0=3, Y_0=4', 'X_0=1, Y_0=1')
xlabel('concentration X [A.U.]');
ylabel('concentration Y [A.U.]');
title('phase space plot for X_0=Y_0=1, A=1, B=1.7, k_i=1 \forall i');
end
function dy = bruesselator(t,y,k1,k2,k3,k4,A,B)
dy = zeros(2,1); % a column vector
dy(1) = k1*A - k2*B*y(1) + k3*y(1)*y(1)*y(2) - k4*y(1);
dy(2) = k2*B*y(1) -k3*y(1)*y(1)*y(2);
end
Licensing[edit]
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
Attribution: Jan Krieger
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 17:37, 4 August 2012 | 744 × 580 (233 KB) | Jkrieger (talk | contribs) | {{Information |Description ={{en|1=solution of "brusselator" differential equations for different conditions}} |Source ={{own}} |Author =Jkrieger |Date =2012-08-04 |Permission = |other_versions =[[:Fil... |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on cs.wikipedia.org
- Usage on de.wikipedia.org
- Usage on en.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on nl.wikipedia.org
- Usage on www.wikidata.org