In-band disruption of a nonlinear circuit using optimal forcing functions

Abstract

In this paper we illustrate a novel method for studying the roleof complex dynamics in practical nonlinear systems of a certain form: Hamiltoniansystems with a homoclinic connexion, subject to forcing and damping.We derive a set of optimal forcing functions which are better than any comparablewaveform at inducing complex dynamics in the system in question viaa break-up of the homoclinic orbit. These forcing functions are then used toinvestigate a practical problem relating to complex dynamics in a nonlinearsystem: how to achieve in-band disruption of a common nonlinear circuit, thephase-locked loop. This problem is chosen both for its intrinsic interest andas a motivational example of how such optimal forcing functions can be usedto understand better complex dynamics in practical nonlinear systems. Numericaland experimental results are reported for a prototypical circuit whichvalidate our approach. The importance and potential benefits of such an approachare discussed.