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混沌系统中的周期轨道以低精度模拟.

Milan Klöwer1,2, Peter V Coveney3,4,5, E Adam Paxton6

  • 1Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, UK. milank@mit.edu.

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在混乱系统中使用低精度数字的模拟可以导致更短,有问题的周期轨道. 随机圆和增加的系统复杂性,而不仅仅是精度,影响模拟保真.

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科学领域:

  • 计算物理 计算物理
  • 动态系统理论 动态系统理论
  • 数字分析 数字分析

背景情况:

  • 混乱的动态系统表现出对其行为至关重要的非周期性解决方案.
  • 有限精度的模拟,特别是低精度格式的模拟,可以引入人工周期性.
  • 随着低精度计算的趋势,混乱系统模拟的忠实性受到质疑.

研究的目的:

  • 调查各种数字格式和精度对混乱系统模拟的影响.
  • 在混乱的动态系统中分析低精度模拟的忠实性.
  • 了解精度,系统复杂性和模拟精度之间的相互作用.

主要方法:

  • 使用浮动,定位和对数固定点格式的物流地图和泛 Bernoulli 地图的模拟.
  • 在不同的数值精度中分析轨道周期性和忠实性.
  • 用不同数量的变量对洛伦茨1996系统进行研究,以评估复杂性效应.

主要成果:

  • 更高的精度提高了模拟,但随机圆可以防止周期轨道即使在低精度.
  • 在像洛伦兹1996这样的大型系统中,轨道周期随着变量数的增加而呈指数增长.
  • 增加的系统复杂性 (更多的变量) 提高了不变量测量近似度,而不是提高了精度.

结论:

  • 混沌系统的低精度模拟可能会产生有问题的周期轨道,挑战模拟保真度.
  • 系统复杂性显著影响轨道长度和混沌系统中的不变量近似度.
  • 对于大规模模型,由于计算限制,人工周期性不太可能成为首要问题,但与连续性解决方案的偏差仍然是一个开放的问题.