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arXiv · 1601.00714

Systematic Measures of Biological Networks, Part I: Invariant measures and Entropy

Yao Li·Yingfei Yi
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Abstract

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.

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Yao Li, Yingfei Yi. 2016-06-10. Systematic Measures of Biological Networks, Part I: Invariant measures and Entropy. https://arxiv.org/abs/1601.00714

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