Updating the parameter of ODE45

I have an ODE system such as

b=1;
f = @(t,x) -(b/N)*x(1)*x(2);
ODE45

I want to write a loop that changes the value of b. But it does not seem to me that just changing the value of b will not update the equation f thus the solution.

b=2;
f = @(t,x) -(b/N)*x(1)*x(2)
ODE45

What should be done here?

[alpedhuez]

Maybe Pass Extra Parameters to ODE Function at https://www.mathworks.com/help/matlab/ref/ode45.html#bu3uhuk?

[Star Strider]

That is the best solution. Include both constants in the argument list:

f = @(t,x,b,N) -(b/N)*x(1)*x(2);

then proceed as in the documentation example.

Answer 1

[Star Strider]

Actually, ‘f’ needs to be a (2x1) matrix, since there are two values of ‘x’, and they both need to be defined, so something like this will work:

f = @(t,x,b,N) [x(1); -(b/N)*x(1)*x(2)];
tspan = [0 5];
ic = rand(2,1);
b = rand;
N = 42;
[t,x] = ode45(@(t,x)f(t,x,b,N), tspan, ic);

I am not certain what you are doing, so this may need to be changed. However to integrate two dependent variables, the ODE function has to have that structure, even if you only use the ‘x(:,2)’ result. I would need to know the original differential equation to know if this is correct for it.

[alpedhuez]

So the equations are

f1 = @(t,x) -(b/N)*x(1)*x(2)
f2 = @(t,x) (b/N)*x(1)*x(2)-(r+d)*x(2);
f3 = @(t,x) r*x(2);
f4 =  @(t,x) d*x(2);
f = @(t,x) [f1(t,x);
            f2(t,x);
            f3(t,x);
            f4(t,x)];
        

So to parameterize with b, we have

f1 = @(b,t,x) -(b/N)*x(1)*x(2)
f2 = @(b,t,x) (b/N)*x(1)*x(2)-(r+d)*x(2);
f3 = @(b,t,x) r*x(2);
f4 =  @(b,t,x) d*x(2);
f = @(b,t,x) [f1(b,t,x);
            f2(b,t,x);
            f3(b,t,x);
            f4(b,t,x)];
        

Is it correct?

[Star Strider]

‘Is it correct?’

I really cannot say, because I have no idea what you are doing. That construction definitely appears to be unusual, to say the least. I have no idea what the original equations are, so that is all that I can say about it. In any event, they all need to be parameterised as functions of ‘r’, ‘d’ and ‘N’ as well.

My opinions aside, run it and see if it gives the result you want and expect.

[alpedhuez]

This seems to work:

f = @(t,x,b,d,r,N) [-(b/N)*x(1)*x(2);(b/N)*x(1)*x(2)-(r+d)*x(2);r*x(2);d*x(2)]

[Star Strider]

That definitely makes sense!

I am still not certain what you are modeling, however that is definitely the correct way to write the ODE function.