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09 February 2025
 
  » arxiv » 1109.0130

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On the numerical simulation of propagation of micro-level uncertainty for chaotic dynamic systems
S.J. Liao ;
Date 1 Sep 2011
AbstractIn this paper, a fine numerical algorithm, namely the "clean numerical simulation" (CNS), is proposed to accurately simulate the propagation of micro-level uncertainty of chaotic dynamic systems. The chaotic Hamiltonian H’enon-Heiles system for motion of stars orbiting in a plane about the galactic center is used as an example to show the validity of the CNS. It is found that, due to the sensitive dependence on initial condition (SDIC) of chaos, the micro-level inherent uncertainty of the position and velocity of a star transfers into the macroscopic randomness of motion. Thus, chaos is a bridge from the micro-level inherent uncertainty to the macroscopic randomness in nature. This provides us a new explanation to the SDIC of chaos from the physical viewpoint.
Source arXiv, 1109.0130
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