Title: A food chain model with prey-taxis and chemotaxis

Authors: Manjun Ma; Yazhou Han; Jicheng Tao; Delin Wu

Addresses: Department of Mathematics, College of Sciences, China Jiliang University, Hangzhou, Zhejiang, 310018, China ' Department of Mathematics, College of Sciences, China Jiliang University, Hangzhou, Zhejiang, 310018, China ' Department of Mathematics, College of Sciences, China Jiliang University, Hangzhou, Zhejiang, 310018, China ' Department of Mathematics, College of Sciences, China Jiliang University, Hangzhou, Zhejiang, 310018, China

Abstract: From the dynamic point of view we construct a food chain model with chemotaxis and investigate theoretically and numerically its steady states. Our results show how the combined action of the death rates, chemotaxis, diffusivity and predator-prey interactions influence the survival ability of multiple consumer levels in a closed ecological system with self-produced nutriment. Furthermore, the food chain length of our model can be determined by the coexistence conditions of all consumer levels. The analytical results are corroborated by numerical simulations.

Keywords: food chain models; modelling; self-produced nutriment; chemotaxis; steady state; index theory; death rates; diffusivity; predator-prey interaction; survival ability; multiple consumer levels; numerical simulation.

DOI: 10.1504/IJMIC.2013.055436

International Journal of Modelling, Identification and Control, 2013 Vol.19 No.3, pp.235 - 247

Published online: 27 Sep 2014 *

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