Inducing Chaos in Systems Using Resonant Perturbations

A chaotic system is one whose long term behavior is unpredictable and is sensitive to the initial conditions. This thesis explores the idea of inducing chaos in systems as a means to render them inoperable. The idea is to use resonant external perturbations to drive nonlinear oscillators into progressively higher resonant states and eventually into chaos. The advantage of this approach over conventional schemes which use high amplitude signals to jam circuits is that relatively weaker signals can be used to induce chaos in systems that need to operate in a restricted parameter regime of order. Weak periodic signals with time varying frequency are used to induce chaos in circuits which are by themselves incapable of exhibiting any chaotic behavior in the region of operation. This thesis also presents an experimental verification of the idea of inducing chaos using resonant perturbations by using a Duffing oscillator along with a phase locked loop. It is seen that resonant perturbations can indeed drive the system into chaos from a periodic state while random perturbations cannot achieve the same effect. This setup makes it possible to design systems that are small and consume very little power which makes them suitable as defensive systems on mobile platforms such as aircraft.