Scaling of Lyapunov exponents of coupled chaotic systems

We develop a statistical theory of the coupling sensitivity of chaos, The e ffect was first described by Daido [Prog. Theor. Phys. 72, 853 (1984)]; it appears as a logarithmic singularity in the Lyapunov exponent in coupled ch aotic systems at very small couplings. Using a continuous-time stochastic m odel for the coupled systems we derive a scaling relation for the largest L yapunov exponent. The singularity is shown to depend on the coupling and th e systems' mismatch. Generalizations to the cases of asymmetrical coupling and three interacting oscillators are considered, too. The analytical resul ts are confirmed by numerical simulations.