Stochastic representation of chaos using terminal attractors

Michail Zak

Chaos, Solitons & Fractals, 2005, vol. 24, issue 3, 863-868

Abstract: A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:24:y:2005:i:3:p:863-868

DOI: 10.1016/j.chaos.2004.09.098

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