# American Institute of Mathematical Sciences

May  2002, 2(2): 221-242. doi: 10.3934/dcdsb.2002.2.221

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

 1 Department of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom, United Kingdom 2 Department of Electronic and Eletrical Engineering, University College London, London, WC1E 7JE, United Kingdom 3 Department of Electrical Engineering, University College London, London, WC1E 7JE, United Kingdom

Received  April 2001 Revised  October 2001 Published  February 2002

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.
Citation: S.M. Booker, P.D. Smith, P. Brennan, R. Bullock. In-band disruption of a nonlinear circuit using optimal forcing functions. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 221-242. doi: 10.3934/dcdsb.2002.2.221
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