title: The transition between strong and weak chaos in delay systems: Stochastic modeling approach.
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.
authors.affiliation: Institute for Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), Campus University of the Balearic Islands, 07122 Palma de Mallorca, Spain.
authors.forename: Thomas
authors.initials: T
authors.lastname: Jüngling
authors.affiliation: Institute for Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany.|Department of Physics, Duke University, 120 Science Dr., Durham, North Carolina 27708, USA.
authors.forename: Otti
authors.initials: O
authors.lastname: D'Huys
authors.affiliation: Institute for Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Kinzel