The transition between strong and weak chaos in delay systems: stochastic modeling approach


We investigate the scaling behavior of the maximal Lyapunov exponent in chaotic systems with time delay. In the large-delay limit, it is known that one can distinguish between strong and weak chaos depending on the delay scaling, analogously to strong and weak instabilities for steady states and periodic orbits. Here we show that the Lyapunov exponent of chaotic systems shows significant differences in its scaling behavior compared to constant or periodic dynamics due to fluctuations in the linearized equations of motion. We reproduce the chaotic scaling properties with a linear delay system with multiplicative noise. We further derive analytic limit cases for the stochastic model illustrating the mechanisms of the emerging scaling laws.

Publication DOI:
Divisions: College of Engineering & Physical Sciences
Additional Information: ©2015 American Physical Society
Publication ISSN: 1550-2376
Last Modified: 08 Jan 2024 08:31
Date Deposited: 10 Feb 2020 13:27
PURE Output Type: Article
Published Date: 2015-06-29
Authors: Jüngling, Thomas
D'Huys, Otti (ORCID Profile 0000-0001-7498-6771)
Kinzel, Wolfgang



Version: Published Version

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