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 language | English |
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Article number | 062918 |
Journal | Physical Review E |
Volume | 91 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Jun 2015 |
Externally published | Yes |
Keywords
- Numerical simulations of chaotic systems
- Delay and functional equations
- Complex systems
- Fluctuation phenomena random processes noise and Brownian motion