Classical Mechanics (Kibble & Berkshire) · Problem 8.11

The energy principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · poincare-bendixson-limit-cycle

Problem

Use Poincar\'e--Bendixson to show that the system x˙=x−y−(x2+4y2)x,y˙=x+y−(x2+4y2)y,\dot{x} = x - y - (x^2 + 4y^2)x, \qquad \dot{y} = x + y - (x^2 + 4y^2)y, has a limit cycle lying in the annulus 12<r<1\tfrac{1}{2} < r < 1.

Related theory

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