Does anyone know in general how to find a Liapunov function when given a system of differential equations?
For example, how would I find a strict Liapunov function for the equilibrium point (0,0) of and ?
I don't think you will have much luck in finding a Lyapunov function for the general nonlinear case. You could try only if the known theorem about the eigenvalues of the linearized problem does not apply.
Which is not the case here. If we call and , the eigenvalues of are negative, and so
the origin is asymptotically stable.
and as long as and , then you have a strict Lyapunov function and can deduce the the origin is asymptotically stable.