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

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Stochastic Modeling
Delay Systems
Scaling Behavior
System Modeling
Lyapunov Exponent
Chaotic System
chaos
Chaos
Scaling
scaling
Multiplicative Noise
Scaling Laws
Periodic Orbits
Stochastic Model
Time Delay
Equations of Motion
Linear Systems
exponents
Fluctuations
orbits

Cite this

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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.",
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The transition between strong and weak chaos in delay systems: stochastic modeling approach. / Jüngling, Thomas; D'Huys, Otti; Kinzel, Wolfgang.

In: Physical Review E, Vol. 91, 062918, 29.06.2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The transition between strong and weak chaos in delay systems: stochastic modeling approach

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AU - D'Huys, Otti

AU - Kinzel, Wolfgang

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N2 - 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.

AB - 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.

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