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Macroscopic rivers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1493)

Abstract

We present a mathematical model for the “river-phenomenon”: striking concentrations of trajectories of ordinary differential equations. This model of “macroscopic rivers” is formulated within nonstandard analysis, and stated in terms of macroscopes and singular perturbations. For a subclass, the “regular” macroscopic rivers, we give necessary and sufficient conditions for their existence, and ways to determine their asymptotic behaviour.

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© 1991 Springer-Verlag

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van den Berg, I.P. (1991). Macroscopic rivers. In: Benoît, E. (eds) Dynamic Bifurcations. Lecture Notes in Mathematics, vol 1493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085032

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  • DOI: https://doi.org/10.1007/BFb0085032

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54900-0

  • Online ISBN: 978-3-540-46471-6

  • eBook Packages: Springer Book Archive