Journal of Mathematical Biology

, Volume 24, Issue 5, pp 479–523

Effects of noise on some dynamical models in ecology

  • W. M. Schaffer
  • S. Ellner
  • M. Kot

DOI: 10.1007/BF00275681

Cite this article as:
Schaffer, W.M., Ellner, S. & Kot, M. J. Math. Biology (1986) 24: 479. doi:10.1007/BF00275681


We investigate effects of random perturbations on the dynamics of one-dimensional maps (single species difference equations) and of finite dimensional flows (differential equations for n species). In particular, we study the effects of noise on the invariant measure, on the “correlation” dimension of the attractor, and on the possibility of detecting the nonlinear deterministic component by applying reconstruction techniques to the time series of population abundances. We conclude that adding noise to maps with a stable fixed-point obscures the underlying determinism. This turns out not to be the case for systems exhibiting complex periodic or chaotic motion, whose essential properties are more robust. In some cases, adding noise reveals deterministic structure which otherwise could not be observed. Simulations suggest that similar results hold for flows whose attractor is almost two-dimensional.

Key words

Nonlinear dynamicsNoiseChaosEcology

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • W. M. Schaffer
    • 1
    • 2
  • S. Ellner
    • 3
  • M. Kot
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyThe University of ArizonaTucsonUSA
  2. 2.Program in Applied MathematicsThe University of ArizonaTucsonUSA
  3. 3.Department of Applied MathematicsWeizmann Institute of ScienceRehovotIsrael
  4. 4.Biomathematics Program, Department of StatisticsNorth Carolina State UniversityRaleighUSA