Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:C3L-B
Session:
Number:C3L-B1
Re-examination of evidence for low-dimensional chaos in the Canadian lynx data
Michael Small, Cristian Carmeli,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
The time series of the annual number of Canadian lynx caught by the Hudson Bay company between 1821 and 1935 exhibits pseudo-cyclic behaviour and has long been considered as an archetypal example of irregularly fluctuating population dynamics. Recently proposed global polynomial models of this data have been found to exhibt chaotic dynamics and were therefore presented as direct evidence of chaos in a real ecosystem. In this paper we re-examine that evidence by constructing global radial basis models subject to information theoretic parameter constraints. We find that the models exhibit very good agreement with the data and are able to accurately reproduce the qualitative long term dynamical behaviour. The models also often exhibit “almost” chaotic dynamics, either: (a) very long period periodicity, (b) a periodic orbit embedded in a dissipative mixing region, or (c) very long time transient irregular aperiodic dynamics with an asymptotically periodic orbit. In each case the dynamics exhibit a very rich range of behaviour and can also provide a qualitatively accurate deterministic model of the apparently chaotic dynamics when subjected to a delay reconstruction. We conclude that, while the data and these models are consistent with the hypothesis of chaos in a real ecosystem, the data may also be adequately explained by periodic “almost chaotic” behaviour.