Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Noise-induced suppression of periodic travelling waves in oscillatory reaction–diffusion systems

Michael Sieber

Michael Sieber

Institute of Environmental Systems Research, Department of Mathematics and Computer Science, University of Osnabrück, 49076 Osnabrück, Germany

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,
Horst Malchow

Horst Malchow

Institute of Environmental Systems Research, Department of Mathematics and Computer Science, University of Osnabrück, 49076 Osnabrück, Germany

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and
Sergei V. Petrovskii

Sergei V. Petrovskii

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

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    Ecological field data suggest that some species show periodic changes in abundance over time and in a specific spatial direction. Periodic travelling waves as solutions to reaction–diffusion equations have helped to identify possible scenarios, by which such spatio-temporal patterns may arise. In this paper, such solutions are tested for their robustness against an irregular temporal forcing, since most natural populations can be expected to be subject to erratic fluctuations imposed by the environment. It is found that small environmental noise is able to suppress periodic travelling waves in stochastic variants of oscillatory reaction–diffusion systems. Irregular spatio-temporal oscillations, however, appear to be more robust and persist under the same stochastic forcing.

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