American Institute of Mathematical Sciences

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

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

S.M. Booker 1, , P.D. Smith 1, , P. Brennan 2, and  R. Bullock 3,

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.
Keywords: Circuit disruption, homoclinic tangle., complex dynamics.
Mathematics Subject Classification: 37D45, 37G15, 94C9.
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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