Use Lyapunov stability theory to investigate the stability of t... | Filo

Question 5: For each of the following systems: (1) ẋ1 = -x1 x1^2 ẋ2 = -x2 (3) ẋ1 = -x1 x1^2 x2 ẋ2 = -x2 x1 (2) ẋ1 = (x1 - x2)(x1^2 x2^2 - 1) ẋ2 = (x1 x2)(x1^2 x2^2 - 1) (4) ẋ1 = -x1 - x2^2 ẋ2 = x1 - x2^3a) Using Lyapunov theory, show that the origin is asymptotically stable. Investigatethe global asymptotic stability of the system.b) If any of the equilibrium points is L.A.S., then estimate the region of attraction.