Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems

Details Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems

2010-03-10

arxiv.org/abs/1003.2013v3

Nonlinear Sciences

Chaotic Dynamics

4pages, 2 figures accepted to CCP 2009 full paper

Scientific paper

10.1016/j.cpc.2010.07.044

In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method for searching these rare trajectories is developed; the method is based on multicanonical Monte Carlo and can estimate the probability of initial conditions that lead to trajectory fragments of a given level of chaoticity. The proposed method is successfully tested with four-dimensional coupled standard maps, where probabilities as small as $10^{-14}$ are estimated.

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