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Quantification of the spatial aspect of chaotic dynamics in biological and chemical systems

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Abstract

The need to study spatio-temporal chaos in a spatially extended dynamical system which exhibits not only irregular, initial-value sensitive temporal behavior but also the formation of irregular spatial patterns, has increasingly been recognized in biological science. While the temporal aspect of chaotic dynamics is usually characterized by the dominant Lyapunov exponent, the spatial aspect can be quantified by the correlation length. In this paper, using the diffusion-reaction model of population dynamics and considering the conditions of the system stability with respect to small heterogeneous perturbations, we derive an analytical formula for an ‘intrinsic length’ which appears to be in a very good agreement with the value of the correlation length of the system. Using this formula and numerical simulations, we analyze the dependence of the correlation length on the system parameters. We show that our findings may lead to a new understanding of some well-known experimental and field data as well as affect the choice of an adequate model of chaotic dynamics in biological and chemical systems.

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Authors and Affiliations

  1. Shirshov Institute of Oceanology, Russian Academy of Science, Nakhimovsky Prospekt 36, Moscow, 117218, Russia

    Sergei Petrovskii

  2. Ecological Complexity and Modeling Laboratory, Department of Botany & Plant Sciences, University of California, Riverside, CA, 92521-0124, USA

    Sergei Petrovskii & Bai-Lian Li

  3. Institute for Environmental Systems Research, Department of Mathematics, Osnabrück University, Osnabrück, D-49069, Germany

    Horst Malchow

Authors
  1. Sergei Petrovskii
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  2. Bai-Lian Li
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  3. Horst Malchow
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Correspondence to Sergei Petrovskii.

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Petrovskii, S., Li, BL. & Malchow, H. Quantification of the spatial aspect of chaotic dynamics in biological and chemical systems. Bull. Math. Biol. 65, 425–446 (2003). https://doi.org/10.1016/S0092-8240(03)00004-1

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  • DOI: https://doi.org/10.1016/S0092-8240(03)00004-1

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