Existence of unbounded solutions for small initial functions in the
van der Pol equation with delayed feedback

Delayed feedback is known as one of useful chaos control methods and
there has been much work on the topic. On the other hand, the van der
Pol equation is a model of electric circuits and is one of classical
and important nonlinear systems. Its dynamics is known to be very
simple. For example, it can have an equilibrium and periodic orbit and
only one of them can be an attractor. In this thesis we study the van
der Pol equation subjected to delayed feedback and show that there
exist unbounded solutions for small initial conditions and initial
functions. This is in contrast to the original equation in which
solutions with small initial conditions go to the equilibrium or
periodic orbits. We also give numerical simulation results to
demonstrate our theoretical result.