We consider coupled map lattices of the type $x_i(n+1\mathrm{})=(1-\epsilon )f\left(x_i\right(n\left)\right)+\left(\epsilon /2\right)\left[f\right(x_{i-1\mathrm{}}\left(n\right))+f(x_{i+1\mathrm{}}\left(n\right)\left)\right]$, where for concreteness we take $f\left(x\right)=1-\left(\mu /4\right)|1-2x{|}^p$, with $p>\mathrm{}1\mathrm{}$. We show that near $\epsilon =0\mathrm{}$ (no coupling) and $\mu =4\mathrm{}$ the envelope of the largest Lyapunov exponent of the full system obeys the scaling law $\overline{\Lambda }={\Lambda }_0-[a\epsilon +b(4-\mu ){]}^{1/p}$. We further argue that this law is universal in that it is independent of the details of $f\left(x\right)$ insofar as $f\left(x\right)$ has a single critical point $x_c$ in the interval $[0,1]$ and its lowest order power expansion about $x_c$ has the form $|{x-x}_c{|}^p$. The dependence of $\overline{\Lambda }$ on the size of the lattice as well as on the range of the coupling is also discussed.

• Received 25 August 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.1808