  In this work we present a theoretical and numerical study of the behaviour of
the maximum Lyapunov exponent for a generic coupled-map-lattice in the
weak-coupling regime. We explain the observed results by introducing a suitable
continuous-time formulation of the tangent dynamics. The first general result
is that the deviation of the Lyapunov exponent from the uncoupled-limit limit
is function of a single scaling parameter which, in the case of strictly
positive multipliers, is the ratio of the coupling strength with the variance
of local multipliers. Moreover, we find an approximate analytic expression for
the Lyapunov exponent by mapping the problem onto the evolution of a chain of
nonlinear Langevin equations, which are eventually reduced to a single
stochastic equation. The probability distribution of this dynamical equation
provides an excellent description for the behaviour of the Lyapunov exponent.
Furthermore, multipliers with random signs are considered as well, finding that
the Lyapunov exponent still depends on a single scaling parameter, which
however has a different expression.
