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Periodic solutions for Van der Pol equation with time delay. (English) Zbl 1210.34096
Summary: For Van der Pol equations with distributed delay, when the distributed delay kernel is the general gamma distributed delay kernel, existence and stability of a periodic solution are obtained by using the linear chain trick and geometric singular perturbation theory. On the other hand, for Van der Pol equations with discrete delay, existence and stability are proved by employing a technique which is based on the inertial manifold. Finally, numerical simulations are also given to illustrate the results.

MSC:
34K13 Periodic solutions to functional-differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
34C45 Invariant manifolds for ordinary differential equations
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