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Applications of Nonlinear Dynamics pp 263–272Cite as

Resonance Curves of Multidimensional Chaotic Systems

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Part of the book series: Understanding Complex Systems ((UCS))

Abstract

We study resonance curves of nonlinear dynamical systems with chaotic forcing functions. We use the calculus of variations to determine the forcing function that induces the largest response. We compute the resonant forcing for a set of model systems and determine the response of the dynamical system to each forcing function. We show that the response is largest if the model system matches the dynamical system. We find that the signal to noise ratio is particularly large if one of the Lyapunov exponents is large.

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Author information

Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

    Glenn Foster

Authors
  1. Glenn Foster
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  2. Alfred W. Hübler
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  3. Karin Dahmen
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Editor information

Editors and Affiliations

  1. Space and Naval Warfare Systems Center Code 2373, 53560 Hull Street, San Diego, CA 92152-5001, USA

    Visarath In  & Patrick Longhini  & 

  2. Department of Mathematics & Statistics, San Diego State University, San Diego, CA 92182-7720, USA

    Antonio Palacios

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Foster, G., Hübler, A.W., Dahmen, K. (2009). Resonance Curves of Multidimensional Chaotic Systems. In: In, V., Longhini, P., Palacios, A. (eds) Applications of Nonlinear Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85632-0_21

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