Linear and nonlinear response of discrete dynamical systems II: Chaotic attractors View Full Text


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Article Info

DATE

1984-06

AUTHORS

T. Geisel, J. Heldstab, H. Thomas

ABSTRACT

We investigate the average response to small external perturbations for discrete dynamical systems with chaotic attractors. The average linear response satisfies a fluctuation theorem, and in general diverges exponentially in the long-time limitt→∞. It vanishes identically for allt>0 only in a number of special cases including the logistic model with bifurcation parameter α=4. The nonlinear response turns out to be crucial. Its average is analyzed for a time-localized (pulse) perturbation. Near the onset of chaos it exhibits universal scaling behaviour expressed by two critical exponents. For static perturbations the resulting dynamics is extremely sensitive to the perturbation strength. More... »

PAGES

165-178

References to SciGraph publications

  • 1983-05. Analytic study of chaos of the tent map: Band structures, power spectra, and critical behaviors in JOURNAL OF STATISTICAL PHYSICS
  • 1978-07. Quantitative universality for a class of nonlinear transformations in JOURNAL OF STATISTICAL PHYSICS
  • 1981-09. The influence of noise on the logistic model in JOURNAL OF STATISTICAL PHYSICS
  • 1982-06. Some exact results on discrete noisy maps in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1983-06. Linear and nonlinear response of discrete dynamical systems in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1976-06. Simple mathematical models with very complicated dynamics in NATURE
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    http://scigraph.springernature.com/pub.10.1007/bf01420569

    DOI

    http://dx.doi.org/10.1007/bf01420569

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