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

In this paper we illustrate a novel method for studying the role of complex dynamics in practical nonlinear systems of a certain form: Hamiltonian systems with a homoclinic connexion, subject to forcing and damping. We derive a set of optimal forcing functions which are better than any comparable waveform at inducing complex dynamics in the system in question via a break-up of the homoclinic orbit. These forcing functions are then used to investigate a practical problem relating to complex dynamics in a nonlinear system: How to achieve in-band disruption of a common nonlinear circuit, the phase-locked loop. This problem is chosen both for its intrinsic interest and as a motivational example of how such optimal forcing functions can be used to understand better complex dynamics in practical nonlinear systems. Numerical and experimental results are reported for a prototypical circuit which validate our approach. The importance and potential benefits of such an approach are discussed.