2016/01/05 by Li, Yao, Yi, Yingfei · 1 citation
#34F05 #37H10 #60H10 #92B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1601.00714
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.