Chapter 23. Predictability and Local Control of Low-dimensional Chaos

  1. Heinz G. Schuster
  1. R. H. Doerner

Published Online: 31 MAY 2006

DOI: 10.1002/3527607455.ch23

Handbook of Chaos Control

Handbook of Chaos Control

How to Cite

Doerner, R. H. (1999) Predictability and Local Control of Low-dimensional Chaos, in Handbook of Chaos Control (ed H. G. Schuster), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527607455.ch23

Editor Information

  1. University of Kiel, Institute of Theoretical Physics, Leibnizstr. 15, D-24098 Kiel, Germany

Author Information

  1. Physikalisches Institut der J. W. Goethe-Universität, Robert-Mayer-Strasse 2-4, D-60325 Frankfurt am Main, Germany

Publication History

  1. Published Online: 31 MAY 2006
  2. Published Print: 23 FEB 1999

ISBN Information

Print ISBN: 9783527294367

Online ISBN: 9783527607457



  • low-dimensional chaos;
  • predictability;
  • Lyapunov exponents;
  • entropy algorithm;
  • Hénon map


This chapter contains sections titled:

  • Introduction

  • A definition of predictability

  • Effective Lyapunov exponents

  • Unstable periodic orbits

  • The origin of predictability contours

  • Chaos control in the presence of large effective Lyapunov exponents

    • The local entropy algorithm

    • Experimental results

  • Adaptive orbit correction in chaos control

    • Orbit corrections in the Hénon map

    • Orbit corrections in a changing environment

    • Experimental orbit correction at the driven pendulum

    • Interaction of prediction and control, outlook