(a) Use the Poincaré-Bendixson Theorem and the fact that the planar system ẋ=x-y-x^3 ẏ=x y-y^3 has only the one critical point at the origin to show that this system has a periodic orbit in the annular region A={x ∈𝐑^2 |. 10, ṙ0 on r=1-ϵ; then use the Poincaré-Bendixson theorem to show that this implies that there is a limit cycle in A̅={𝐱 ∈𝐑^2|1 ≤| 𝐱 |≤√(2)} and then show that no limit cycle can have a point in common with either one of the circles r=1 or r=√(2). (b) Show that there is at
(a) Use the Poincaré-Bendixson Theorem and the fact that the plan…
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