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Life on the Edge of Chaos

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Abstract

In this article we consider singularly perturbed systems of ordinary differential equations having one swift and one n (n ≥ 3) slow variable. Conditions for the existence of attractors of hard turbulence type and of on-off intermittency are formulated. It is shown that any finite-dimensional system with chaos can be complemented so that it will have one dimension more and hard turbulence will arise. In other words, we propose one possible way of taking into account rare catastrophic events in systems with complicated behavior.

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Authors
  1. A. Yu. Kolesov
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  2. N. Kh. Rozov
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  3. V. A. Sadovnichiy
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Kolesov, A.Y., Rozov, N.K. & Sadovnichiy, V.A. Life on the Edge of Chaos. Journal of Mathematical Sciences 120, 1372–1398 (2004). https://doi.org/10.1023/B:JOTH.0000016055.44231.af

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  • DOI: https://doi.org/10.1023/B:JOTH.0000016055.44231.af

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