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Noise-induced clustering in Hamiltonian systems

D. V. Makarov·M. Yu. Uleysky·M. V Budyansky·S. V. Prants
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Abstract

The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincaré map, is proposed and justified. Physical manifestations of these regions of stability, the so-called coherent clusters, are demonstrated with two models in ocean physics. We find bunches of sound rays propagating coherently in an underwater waveguide through a randomly fluctuating ocean at long distances. We find clusters of passive particles to be advected coherently by a random two-dimensional flow modelling mixing around a topographic eddy in the ocean.

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D. V. Makarov, M. Yu. Uleysky, M. V Budyansky, S. V. Prants. 2005-07-07. Noise-induced clustering in Hamiltonian systems. https://arxiv.org/abs/nlin/0507010

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