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Scaling of Lyapunov exponents in chaotic delay systems

Research paper by Thomas Jüngling, Wolfgang Kinzel

Indexed on: 12 Oct '12Published on: 12 Oct '12Published in: Nonlinear Sciences - Chaotic Dynamics



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.