Related Experiment Video
Updated: Aug 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Scaling of lyapunov exponents of coupled chaotic systems
1Department of Physics, University of Potsdam, Postfach 601553, D-14415 Potsdam, Germany.
Abstract:
We develop a statistical theory of the coupling sensitivity of chaos. The effect was first described by Daido [Prog. Theor. Phys. 72, 853 (1984)]; it appears as a logarithmic singularity in the Lyapunov exponent in coupled chaotic systems at very small couplings. Using a continuous-time stochastic model for the coupled systems we derive a scaling relation for the largest Lyapunov exponent. The singularity is shown to depend on the coupling and the systems' mismatch. Generalizations to the cases of asymmetrical coupling and three interacting oscillators are considered, too. The analytical results are confirmed by numerical simulations.
Related Concept Videos
Scaling
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Second Order systems I
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Second Order systems II
If ζ...
Plotting and Calibrating the Root Locus
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is observed...

