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DYNAMICS · 1

Flows and invariant sets

11 concepts · 21 questions

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DYNAMICSStep●○○○○new1 Flows and invariant sets
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The problem

Consider x˙=−x+xy2\dot x = -x + xy^2, y˙=−y\dot y = -y. (a) With V=x2+y2V = x^2 + y^2, compute V˙\dot V and show it is negative on the unit disc minus the origin. (b) Deduce a set contained in the basin of the origin. (c) Solve the system explicitly and find the true basin.

Compute V˙\dot V.