Connectance of dynamical systems with increasing number of degrees of freedom

A set of $n$ coupled two-dimensional area-preserving mappings in taken as a model problem for the study of the stochasticity of dynamical systems with $n$ degrees of freedom. The connectance of the system is defined as the percentage of two-dimensional mappings that are directly coupled. This work suggests that large complex dynamical systems may be expected to be stable below some critical level of connectance, but that as the connectance increases above that level they would become unstable.