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
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