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Noise can prevent onset of chaos in spatiotemporal population dynamics

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Abstract

Many theoretical approaches predict the dynamics of interacting populations to be chaotic but that has very rarely been observed in ecological data. It has therefore risen a question about factors that can prevent the onset of chaos by, for instance, making the population fluctuations synchronized over the whole habitat. One such factor is stochasticity. The so-called Moran effect predicts that a spatially correlated noise can synchronize the local population dynamics in a spatially discrete system, thus preventing the onset of spatiotemporal chaos. On the whole, however, the issue of noise has remained controversial and insufficiently understood. In particular, a well-built nonspatial theory infers that noise enhances chaos by making the system more sensitive to the initial conditions. In this paper, we address the problem of the interplay between deterministic dynamics and noise by considering a spatially explicit predator-prey system where some parameters are affected by noise. Our findings are rather counter-intuitive. We show that a small noise (i.e. preserving the deterministic skeleton) can indeed synchronize the population oscillations throughout space and hence keep the dynamics regular, but the dependence of the chaos prevention probability on the noise intensity is of resonance type. Once chaos has developed, it appears to be stable with respect to a small noise but it can be suppressed by a large noise. Finally, we show that our results are in a good qualitative agreement with some available field data.

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Authors and Affiliations

  1. Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK

    S. Petrovskii & A. Morozov

  2. Department of Mathematics and Computer Science, Institute of Environmental Systems Research, 49069, Osnabrück, Germany

    H. Malchow & M. Sieber

Authors
  1. S. Petrovskii
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  2. A. Morozov
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  3. H. Malchow
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  4. M. Sieber
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Correspondence to S. Petrovskii.

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Petrovskii, S., Morozov, A., Malchow, H. et al. Noise can prevent onset of chaos in spatiotemporal population dynamics. Eur. Phys. J. B 78, 253–264 (2010). https://doi.org/10.1140/epjb/e2010-10410-8

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  • DOI: https://doi.org/10.1140/epjb/e2010-10410-8

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