Paper 2, Section II, E
(a) State and prove Dulac's criterion. State clearly the Poincaré-Bendixson theorem.
(b) For and , consider the dynamical system
(i) Use Dulac's criterion to find a range of for which this system does not have any periodic orbit.
(ii) Find a suitable such that trajectories enter the disc and do not leave it.
(iii) Given that the system has no fixed points apart from the origin for , give a range of for which there will exist at least one periodic orbit.
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