Solvable Catalyzed Birth-Death-Exchange Competition Model of Three Species

作     者：WANG Hai-Feng LIN Zhen-Quan GAO Yan ZHANG Heng 

作者机构：Department of Physics Teacthers College Shihezi University Shihezi 832003 China Department of Physics Wenzhou University Wenzhou 325027 China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2009年第52卷第10期

页      面：735-742页

核心收录：

学科分类：081703[工学-生物化工] 08[工学] 0817[工学-化学工程与技术] 0836[工学-生物工程] 080101[工学-一般力学与力学基础] 082203[工学-发酵工程] 0822[工学-轻工技术与工程] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos.10275048,10305009,and 10875086 by the Zhejiang Provincial Natural Science Foundation of China under Grant No.102067 

主　　题：aggregation exchange-driven growth catalysis kinetic behaviour 

摘      要：A competition model of three species in exchange-driven aggregation growth is proposed. In the model, three distinct aggregates grow by exchange of monomers and in parallel, birth of species A is catalyzed by species B and death of species A is catalyzed by species C. The rates for both catalysis processes are proportional to kj^v and ky respectively, where ν（ω） is a parameter reflecting the dependence of the catalysis reaction rate of birth （death） on the catalyst aggregate＇s size. The kinetic evolution behaviors of the three species are investigated by the rate equation approach based on the mean-field theory： The form of the aggregate size distribution of A-species αk（t） is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that （i） in case of ν ≤O, the form of ak （t） mainly depends on the competition between self-exchange of species A and species-C-catalyzed death of species A; （ii） in case of ν 〉 0, the form of αk（t） mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A.