Cyclicity or Chaos? Orbital Forcing Versus Non-Linear Dynamics

  1. P. L. de Boer2 and
  2. D. G. Smith3
  1. D. G. Smith

Published Online: 29 APR 2009

DOI: 10.1002/9781444304039.ch31

Orbital Forcing and Cyclic Sequences

Orbital Forcing and Cyclic Sequences

How to Cite

Smith, D. G. (1994) Cyclicity or Chaos? Orbital Forcing Versus Non-Linear Dynamics, in Orbital Forcing and Cyclic Sequences (eds P. L. de Boer and D. G. Smith), Blackwell Publishing Ltd., Oxford, UK. doi: 10.1002/9781444304039.ch31

Editor Information

  1. 2

    Utrecht, The Netherlands

  2. 3

    London, UK

Author Information

  1. Petroconsultants (UK) Ltd, Europa House, 266 Upper Richmond Road, Putney, London SW15 6TQ, UK

Publication History

  1. Published Online: 29 APR 2009
  2. Published Print: 28 JAN 1994

ISBN Information

Print ISBN: 9780632037360

Online ISBN: 9781444304039



  • orbital forcing versus non-linear dynamics;
  • calculated periods of ‘mesoscale’ sedimentary cycles;
  • Milankovitch machine;
  • fractal properties;
  • non-linear dynamics


Chaos theory (or non-linear dynamics) predicts complex yet non-random output from natural systems in which feedback mechanisms are important. It therefore competes with the Milankovitch hypothesis as an explanation for sedimentary cyclicity. In this paper, the stratigraphic record is presented as the product of a highly complex system of interacting influences, which can be expected to show some of the characteristics of dynamical systems. These include recurrence, fractal-like distribution of stratal properties, low-dimensionality, approximate coincidence in time of diverse phenomena, and problems of distinguishing cause and effect.

Analytical methods to distinguish system-generated information from noise in observational time-series data are at an early stage of development. Graphical methods, however, lend some support to the hypothesis that the ‘Stratigraphy Machine’ has all the characteristics of a non-linear dynamical system. Such systems are usefully conceptualized as comprising coupled oscillators, like a forced pendulum. As such, they are capable of damping out an input forcing signal such as the predicted orbitally mediated changes in solar insolation. Given suitable tuned strength of coupling, they are equally capable of resonating to the same input frequencies. A dynamical systems view of the stratigraphic record, in which the Milankovitch signal may at different times be (i) unambiguously encoded, (ii) cryptic but suspected, or (iii) absent, is therefore qualitatively consistent with the available evidence. Non-linear dynamics could prove to be the reason for the preservation of the orbital signal (and of many other phenomena) in the stratigraphic record. Quantitative demonstration can in future be approached through modelling and simulation.