Noise can prevent onset of chaos in spatiotemporal population dynamics
Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
2 Institute of Environmental Systems Research, Department of Mathematics and Computer Science, Osnabrück University, 49069 Osnabrück, Germany
Corresponding author: a email@example.com
Revised: 26 September 2010
Published online: 3 November 2010
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010