Question: 2. Consider the Hopf normal form u -1 @ u +v v -@ V (a) Show that there exist a periodic solution of period

2. Consider the Hopf normal form u -1 @ u +v v

2. Consider the Hopf normal form u -1 @ u +v v -@ V (a) Show that there exist a periodic solution of period 2/ and amplitude 1. (b) Using the modern Lyapunov approach show that the equilibrium is locally asymptotically stable. (c) Using a barrier function show that the disc of radius 1 is forward invariant.

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