Numerical coalescence of chaotic trajectories

Roth, Bruce N and Wilkinson, Michael (2020). Numerical coalescence of chaotic trajectories. Journal of Physics A: Mathematical and Theoretical, 53(34), article no. 345701.

DOI: https://doi.org/10.1088/1751-8121/ab9bcf

Abstract

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to a universality class of chaotic systems where this numerical coincidence effect can be described by mapping it to a first-passage process. Our results are applicable to aggregation of small particles in random flows, as well as to numerical investigation of chaotic systems.

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