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

Thomas Jüngling, Otti D'Huys, Wolfgang Kinzel

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Article number062918
JournalPhysical Review E
Volume91
DOIs
Publication statusPublished - 29 Jun 2015

Bibliographical note

©2015 American Physical Society

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