Linear and nonlinear response of discrete dynamical systems View Full Text


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Article Info

DATE

1983-06

AUTHORS

J. Heldstab, H. Thomas, T. Geisel, G. Radons

ABSTRACT

We carry out a linear response theory for discrete dynanmical systems with periodic attractors. The symmetry properties of the susceptibility matrix are studied and its eigenvalues and eigenvectors are determined. Close to a period-doubling bifurcation where the susceptibility diverges, its half-width is related to the Lyapunov exponent. At the transition to chaos the susceptibility has some universal behaviour which is described by a critical exponent κ=1−(ln2/lnδ)=0.550193... At the bifurcation points where linear response theory becomes insufficient we also determine the nonlinear response. More... »

PAGES

141-150

References to SciGraph publications

  • 1979-12. The universal metric properties 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
  • 1981-05. Period doubling bifurcations for families of maps on ℝn in JOURNAL OF STATISTICAL PHYSICS
  • 1978-07. Quantitative universality for a class of nonlinear transformations in JOURNAL OF STATISTICAL PHYSICS
  • 1981-06. Chapman-Kolmogorov equation and path integrals for discrete chaos in presence of noise in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1976-06. Simple mathematical models with very complicated dynamics in NATURE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01304096

    DOI

    http://dx.doi.org/10.1007/bf01304096

    DIMENSIONS

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