Solvable Catalyzed Birth-Death-Exchange Competition Model of Three Species |
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Authors: | WANG Hai-Feng LIN Zhen-Quan GAO Yan ZHANG Heng |
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Institution: | 1.Department of Physics, Teacthers College, Shihezi University, Shihezi 832003, China
;2.Department of Physics, Wenzhou University, Wenzhou 325027, China |
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Abstract: | 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 kjυ and kjω respectively, where υ(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 ofA-species ak(t) is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that (i) in case of υ ≤ 0, the form of ak(t) mainly depends on the competition between self-exchange of species A andspecies-C-catalyzed death of species A; (ii) in case of υ>0, the form of ak(t) mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A. |
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Keywords: | aggregation exchange-driven growth catalysis kinetic behaviour |
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