How can I plot a graph by varying two parameters a and b in system of ODE at the same time?

How can I plot a graph by varying two parameters say a and b in the system of ordinary differential equations given below at the same time so that the first line of solution will be when a=1, b=2, the second line of solution will be when a=2, b=3, the third line of solution will be when a=3, b=4 and I will have three lines of solutions on the same graph? I want to plot t against

function  SYSTEM1ODE ()
global C a b d e g 

clear all
 clc
tspan=[0 5];


 a=1;d=2;C=10000;e=5;g=1;


for b= 2:1:4
[t,x]=ode45(@modmat, tspan, [1200;1150;1000])

 plot(t,x(:,2),'linewidth',1.5)
 xlabel('Time (Days)'),ylabel('Amonut (X_2)')

 hold on
end

function xprime = modmat(t,x)
  
xprime=[0;0;0];

xprime(1)=C-a*x(1)-b*x(2)+d*x(1);
xprime(2)=a*x(1)-b*x(2)-(d+e)*x(2);
xprime(3)=e*x(2)-g*x(3);
end
end

How can I add 'a' to it, so that 'a' and 'b' will be varying at the same time and still get three lines of solutions on the same graph?

[Torsten]

Can you include the code for a single combination ? We will show you how to make a loop to use it three times.

[SAHEED AJAO]

Thanks, I can only vary one variable 'b' alone but unable to vary the two at the same time. Here is the code.

function  SYSTEM1ODE ()
global C a b d e g 

clear all
 clc
tspan=[0 5];


 a=1;d=2;C=10000;e=5;g=1;


for b= 2:1:4
[t,x]=ode45(@modmat, tspan, [1200;1150;1000])

 plot(t,x(:,2),'linewidth',1.5)
 xlabel('Time (Days)'),ylabel('Amonut (X_2)')

 hold on
end

function xprime = modmat(t,x)
  
xprime=[0;0;0];

xprime(1)=C-a*x(1)-b*x(2)+d*x(1);
xprime(2)=a*x(1)-b*x(2)-(d+e)*x(2);
xprime(3)=e*x(2)-g*x(3);
end
end

How can I add 'a' to it, so that 'a' and 'b' will be varying at the same time and still get three lines of solutions on the same graph?

Answer 1

[Torsten]

A = [1;2;3];
B = [2;3;4];
C = 10000;
d = 2;
e = 5;
g = 1;
tspan = [0 5];
for i = 1:numel(A)
    a = A(i);
    b = B(i);
    [t,x] = ode45(@(t,x)modmat(t,x,a,b,C,d,e,g),tspan,[1200;1150;1000]);
    plot(t,x(:,2),'linewidth',1.5)
    xlabel('Time (Days)'),ylabel('Amonut (X_2)')
    hold on
end

function xprime = modmat(t,x,a,b,C,d,e,g)
  xprime=[0;0;0];
  xprime(1)=C-a*x(1)-b*x(2)+d*x(1);
  xprime(2)=a*x(1)+b*x(2)-(d+e)*x(2);
  xprime(3)=e*x(2)-g*x(3);
end

[SAHEED AJAO]

Thanks, I am grateful.