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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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Front Math Chin    2009, Vol. 4 Issue (3) : 495-521    https://doi.org/10.1007/s11464-009-0031-7
RESEARCH ARTICLE
How many consumer levels can survive in a chemotactic food chain?
Jing LIU1, Chunhua OU2()
1. Department of Mathematics, Dalian Maritime University, Dalian 116024, China; 2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada
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Abstract

We investigate the effect and the impact of predator-prey interactions, diffusivity and chemotaxis on the ability of survival of multiple consumer levels in a predator-prey microbial food chain. We aim at answering the question of how many consumer levels can survive from a dynamical system point of view. To solve this standing issue on food-chain length, first we construct a chemotactic food chain model. A priori bounds of the steady state populations are obtained. Then under certain sufficient conditions combining the effect of conversion efficiency, diffusivity and chemotaxis parameters, we derive the co-survival of all consumer levels, thus obtaining the food chain length of our model. Numerical simulations not only confirm our theoretical results, but also demonstrate the impact of conversion efficiency, diffusivity and chemotaxis behavior on the survival and stability of various consumer levels.
Keywords Food chain length      chemotaxis      stability      priori estimates      fixedpoint index theory     
Corresponding Author(s): OU Chunhua,Email:ou@mun.ca   
Issue Date: 05 September 2009
 Cite this article:   
Jing LIU,Chunhua OU. How many consumer levels can survive in a chemotactic food chain?[J]. Front Math Chin, 2009, 4(3): 495-521.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0031-7
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I3/495
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