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Q1. Consider the nonlinear system given by *1 = x (x2 - 3) *2 = 25 - x - x a. Find all possible equilibrium points of the system. Show them on the x1 - x2 axis. Assign labels to the equilibrium points you find as xe, xe..etc. and use these labels in the rest of this question to identify the equilibrium points. b. What can you say about the (asymptotic) stability (i.s.L.) of the equilibrium point(s) using Lyapunov's indirect method? c. Suppose that someone tells you that this system has a periodic trajectory in the form of a circle centered at the point x1 = x2 = 2 with radius R. Find the possible range of values for the radius R based on only the index theorem. d. Repeat part-c using Bendixson's theorem, i.e., find the possible range of values for the radius R based on only the Bendixson's theorem. Q1. Consider the nonlinear system given by *1 = x (x2 - 3) *2 = 25 - x - x a. Find all possible equilibrium points of the system. Show them on the x1 - x2 axis. Assign labels to the equilibrium points you find as xe, xe..etc. and use these labels in the rest of this question to identify the equilibrium points. b. What can you say about the (asymptotic) stability (i.s.L.) of the equilibrium point(s) using Lyapunov's indirect method? c. Suppose that someone tells you that this system has a periodic trajectory in the form of a circle centered at the point x1 = x2 = 2 with radius R. Find the possible range of values for the radius R based on only the index theorem. d. Repeat part-c using Bendixson's theorem, i.e., find the possible range of values for the radius R based on only the Bendixson's theorem

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