Nawaj Sarif

I'm unsure. But, consider such nonlinear system. Does a limit exist at the equilibrium point (0, 0) in the Jacobian matrix?

Where all derivatives are evaluated at the equilibrium point x=x_{\rm e}\ . Its eigenvalues determine linear stability properties of the equilibrium. An equilibrium is asymptotically stable if all eigenvalues have negative real parts; it is unstable if at least one eigenvalue has positive real part.The Jacobian matrix at each equilibrium is J=f'(x)\ . An equilibrium is asymptotically stable when f'(x)