Periodic trajectories of distributed parameter biochemical systems with time delay

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• 作者：A.K. Drame^a ; ^{adrame@lagcc.cuny.edu} ; D. Dochain^b ; ^{deni.dochain@uclouvain.be} ; J.J. Winkin^c ; ^{joseph.winkin@fundp.ac.be} ; P.R. Wolenski^d ; ^{wolenski@math.lsu.edu}
• 关键词：Time delay ; Periodic solutions ; Biochemical reactor ; Partial functional differential equations
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 March, 2012
• 卷：218
• 期：14
• 页码：7395-7405
• 文件大小：313 K

摘要

This paper deals with a model of a biochemical reactor system with distributed parameters and with a time delay in the growth response. Time delay has been introduced in microbial growth systems to explain the time lapse between the consumption of (liquid) substrate and its conversion to (solid) biomass. We study here the properties of the resulting system of partial functional differential equations. We first prove the existence, positivity, and a compactness property of the system trajectories. We then prove the existence of periodic solutions of the system for large values of the delay. Numerical simulations illustrate the existence of such solutions.