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Summary
| Description |
English: solution of "brusselator" differential equations for different conditions |
| Date | |
| Source | Own work |
| Author | Jkrieger |
| Other versions | File:bruesselator_de.svg |
Source Code
Source code
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
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
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:37, 4 August 2012 | | 744 × 580 (233 KB) | Jkrieger | {{Information |Description ={{en|1=solution of "brusselator" differential equations for different conditions}} |Source ={{own}} |Author =Jkrieger |Date =2012-08-04 |Permission = |other_versions =[[:Fil... |
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