Scaling of Lyapunov exponents of coupled chaotic systems
- 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.
| Author details: | Rüdiger Zillmer, Volker AhlersORCiDGND, Arkadij PikovskijORCiDGND |
|---|---|
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2000 |
| Publication year: | 2000 |
| Release date: | 2017/03/24 |
| Source: | Physical Review / E. - 61 (2000), 1, S. 332 - 341 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |
