Find a trapping region, and apply the Poincare-Bendixon Theorem to prove the exi

Question

Find a trapping region, and apply the Poincare-Bendixon Theorem to prove the existence of
a limit cycle. Hint: try using a rectangle for your bounding region, with two of its sides lying
on x and y axes.

Consider the ODE system x(t), y(t) >= 0 (here, x, y represent chemical concentrations in a certaion reaction): Find a trapping region, and apply the Poincare-Bendixon Theorem to prove the existence of a limit cycle. Hint: try using a rectangle for your bounding region, with two of its sides lying on x and y axes. X = a - x - xy/1 + x^2, y = bx(1 - y/1 + x^2) where parameters a, b > 0 and both

Explanation / Answer

r* is stable and unique -> system has stable limit cycle

given by the circle r=1.

DP(x*) is linearized Poincare map at x*

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