Zeitschrift für Physik B Condensed Matter

, Volume 50, Issue 2, pp 141–150

Linear and nonlinear response of discrete dynamical systems

I. Periodic attractors
  • J. Heldstab
  • H. Thomas
  • T. Geisel
  • G. Radons
Article

DOI: 10.1007/BF01304096

Cite this article as:
Heldstab, J., Thomas, H., Geisel, T. et al. Z. Physik B - Condensed Matter (1983) 50: 141. doi:10.1007/BF01304096

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.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • J. Heldstab
    • 1
  • H. Thomas
    • 1
  • T. Geisel
    • 2
  • G. Radons
    • 2
  1. 1.Institut für Theoretische Physik der UniversitätBaselSwitzerland
  2. 2.Institut für Theoretische Physik der UniversitätRegensburgFederal Republic of Germany

Personalised recommendations