Stability of Systems with Stochastic Delay

Stochastic delay;linear systems;Mechanical Engineering;Engineering;Mechanical Engineering

Sadeghpour, MehdiLiu, Allen Po-Chih ;

University of Michigan

关键词: Stochastic delay;    linear systems;    Mechanical Engineering;    Engineering;    Mechanical Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/144051/mehsad_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Stability of systems with stochastic delays is addressed in this dissertation. A lineardelay differential equation is considered where the delay takes values from afinite set of numbers according to a probability distribution function. Exact stabilityconditions for the resulting system are obtained. These conditions dependon the parameters of the system, the delay values and the probability distributionfunction governing the delay. The stability criteria are first obtained in a discretetimesetting after discretizing the continuous-time system. Then, the stability conditionsare obtained in a continuous-time setting where an operator description ofdelay differential equations is used.The stability results are applied to models of gene regulatory networks. The resultscan determine whether a steady state protein production is stable or oscillationsin protein levels may arise as a result of stochastic fluctuations in reactiontimes. Finally, the interplay between noise in the gene expression level and noisein the population level in microbial consortia is investigated. The results suggesta mechanism for creating robust oscillations in multicellular environments.