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Question: dynamical systems n2 systemsphase flow 1 consider the following vector...

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Dynamical Systems: N-2 Systems(Phase Flow)

(1) Consider the following vector field, described in 2D polar coordinates: r˙ = r(1 − r 2 ) + λ r cos θ ˙θ = 1 , where 0 < λ < 1. (a) Show that the radial component of the flow along the circle r = a ≡ √ 1 − λ is outward, and that the radial component along the circle r = b ≡ √ 1 + λ is inward. (b) For λ = 0.8, plot the vector field. (c) Numerically integrate the dynamical system starting from the point (r = 1 , θ = 0, with λ = 0.8 and identify the stable limit cycle.

Explanation for setting up and solving the problem would be greatly appreciated as I still struggle with understanding how to solve these types of problems and how to plot. You can use Mathematica to solve but explanations are still warranted. Thanks for the help!

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