Question

Consider a nonlinear system described by $\dot{x}_1=-x_1+x_2$, $\dot{x}_2=2x_2+x_1^2$ Generate a Liapunov function v(x) and comment on definiteness of the function and stability of equilibrium state.

Answer 1

Find all equilibrium points for each of the following systems. $\dot{x_1} =-x_1+x_2(1+x_1)$, $\dot{x}_2=-3x_1(1-x_1)$