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Discrete Dynamics in Nature and Society - Volume 2015 2015, Article ID 306302, 7 pages -

Research ArticleCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 22 October 2014; Accepted 30 January 2015

Academic Editor: Daniele Fournier-Prunaret

Copyright © 2015 Tiansi Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results.





Autor: Tiansi Zhang, Xuehui Ji, and Bo Li

Fuente: https://www.hindawi.com/



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