  This paper is Part I of a two-part series devoting to the study of systematic
measures in a complex biological network modeled by a system of ordinary
differential equations. As the mathematical complement to our previous work
[31] with collaborators, the series aims at establishing a mathematical
foundation for characterizing three important systematic measures: degeneracy,
complexity and robustness, in such a biological network and studying
connections among them. To do so, we consider in Part I stationary measures of
a Fokker-Planck equation generated from small white noise perturbations of a
dissipative system of ordinary differential equations. Some estimations of
concentration of stationary measures of the Fokker-Planck equation in the
vicinity of the global attractor are presented. Relationship between
differential entropy of stationary measures and dimension of the global
attractor is also given.
