Automating the stability calculation for an ODE

I want to numerically solve an ODE using ODE45. Let's say the ODE is

    function dydt = odefun(t,y,a,b,g,d)
        dydt = [
             y(1)*(a - b*y(2));
            -y(2)*(g - d*y(1));
            ];
    end;

but I will actually work with a much higher dimensional system. Elsewhere, I make the call

  [t,y] = ode45(@(t,y) odefun(t,y,alpha,beta,gamma,delta), [0 tmax], [initialx initialy]);

Currently it runs fine. However, I would like to:

• calculate the Jacobian matrix
• evaluate it at an equilibrium whose coordinates I know
• do standard stability analysis (eigenvalues and eigenvectors)

I don't want to hard-code in the Jacobian, since I will tinker with the differential equation. Getting Matlab to calculate the Jacobian is my current problem. Suggestions would be appreciated.

[Allaka Himabindu]

Hello, Did you figure out any solution for this, I am looking for a similar kind of capability.

Thanks

[Connell McCluskey]

Not yet. For now, I have the Jacobian typed in, so that a change to the differential equation means I have to go and change the Jacobian by hand.