Scaling of Lyapunov exponents in chaotic delay systems

Thomas Jüngling; Wolfgang Kinzel

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arXiv · 1210.3528

Scaling of Lyapunov exponents in chaotic delay systems

Thomas Jüngling·Wolfgang Kinzel

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Abstract

The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and weak chaos, which are the analogy to strong and weak instability of periodic orbits in a delay system. We find significant differences between scaling of exponents in periodic or chaotic systems. We show that chaotic scaling is related to fluctuations in the linearized equations of motion. A linear delay system including multiplicative noise shows the same properties as the deterministic chaotic systems.

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Thomas Jüngling, Wolfgang Kinzel. 2012-10-12. Scaling of Lyapunov exponents in chaotic delay systems. https://arxiv.org/abs/1210.3528

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