Pathway structure determination in complex stochastic networks with non-exponential dwell times
Kolomeisky, Anatoly B.
Analysisﾠof complexﾠnetworksﾠhas been widely used as a powerful tool for investigating various physical, chemical, and biological processes. To understand the emergentﾠpropertiesﾠof these complex systems, one of the most basic issues is to determine the structure andﾠtopologyﾠof the underlyingﾠnetworks.ﾠRecently, a newﾠtheoreticalﾠapproach based on first-passageﾠanalysisﾠhas been developed for investigating the relationship between structure and dynamicﾠpropertiesﾠforﾠnetworkﾠsystems with exponential dwell time distributions. However, many real phenomena involve transitions with non-exponential waiting times. We extend the first-passage method to uncover the structure of distinct pathways in complexﾠnetworksﾠwith non-exponential dwell time distributions. It is found that theﾠanalysisﾠof early time dynamics provides explicit information on the length of the pathways associated to their dynamicﾠproperties.ﾠIt reveals a universal relationship that we have condensed in one general equation, which relates the number of intermediate states on the shortest path to the early time behavior of the first-passage distributions. Ourﾠtheoreticalﾠpredictions are confirmed by extensiveﾠMonte Carlo simulations.