Question

QUESTION 3. Consider the following system (a) Convert to polar coordinates and find a periodic orbit. Write the corresponding periodic solution as a function of time t. (b) Show that the periodic orbit found in (a) is locally asymptotically stable by calculating a Floquet multiplier of the variational equation (or eigenvalue of derivative of Poincaré map) corresponding to (1) at the periodic solution. (c) Can you prove further that all non-zero solutions converge asymptotically to the periodic orbit?

Need answer to part (c).

Answer 1

here (x , y) was any arbitrary nonzero solution and we got as t increases (x(t) , y(t)) converge asymptotically to the periodic orbit, i.e r(t) = 2.

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