Changing a parameter in a differential equation?

My code is below:

Y0=[0;0;1];

tRange=[0,10000];

[tSol,YSol]=ode45(@quantumsystem,tRange,Y0);

x=YSol(:,1);

y=YSol(:,2);

z=YSol(:,3);

plot(tSol,z,'k')

function dYdt = quantumsystem(t,Y);

x=Y(1);

y=Y(2);

z=Y(3);

gamma=1/2;

epsilon=0.1;

c=1;

dtheta=gamma*c/(t^2 + c^2);

dxdt=(-1/epsilon)*y - dtheta*z;

dydt=(1/epsilon)*x;

dzdt=dtheta*x;

dYdt=[dxdt;dydt;dzdt];

end

---

I wish to create a family of graphs, where the parameter "epsilon" is varied. The only way I know how to do this would be to keep redefining the function dYdt, changing epsilon each time.

I was wondering if there was a quicker way to do this. Ideally, something like

Y0=[0;0;1];

tRange=[0,10000];

[tSol,YSol]=ode45(@quantumsystem,tRange,Y0);

x=YSol(:,1);

y=YSol(:,2);

z=YSol(:,3);

epsilon=0.1

plot(tSol,z,'k')

hold on

epsilon=0.01

function dYdt = quantumsystem(t,Y);

x=Y(1);

y=Y(2);

z=Y(3);

gamma=1/2;

c=1;

dtheta=gamma*c/(t^2 + c^2);

dxdt=(-1/epsilon)*y - dtheta*z;

dydt=(1/epsilon)*x;

dzdt=dtheta*x;

dYdt=[dxdt;dydt;dzdt];

end

except that that gives me an error.

I hope my question is clear.

Any help would be much appreciated. Thank you!

Answer 1

[David Goodmanson]

Hi Sean,

you can pass the value of epsilon into the ode function with

[tSol,YSol]=ode45(@(t,Y) quantumsystem(t,Y,epsilon),tRange,Y0);

and

function dYdt = quantumsystem(t,Y,epsilon);
    x=Y(1);
    y=Y(2);
    z=Y(3);
    gamma=1/2;
    c=1;
    dtheta=gamma*c/(t^2 + c^2);
    dxdt=(-1/epsilon)*y - dtheta*z; 
    dydt=(1/epsilon)*x;
    dzdt=dtheta*x;
    dYdt=[dxdt;dydt;dzdt];
end

Since ode45 picks the time increments, different values of epsilon may lead to different lengths of tSol and YSol, but the information is there. One of the easier ways to deal with that issue is to set up a for loop with different values of epsilion and use

plot(tSol,z)
hold on

inside the loop as you are doing, only without the color specification.