Consider differential equation \begin{align}x'&=-t(x+y)\\ y'&=-y+x-y(y^2-6).\end{align} Can some one suggest a lyapunov function for it.
I have examined $V(x,y)=x^2+y^2$ , $V(x,y)=(1+t^2)(x^2+y^2)$ , $V(x,y)=(1+t^2)^2(x^2+y^2)$ but I could not solve the stablity with these functions.
Thanks