The Bifurcation and Control of a Single-Species Fish Population Logistic Model with the Invasion of Alien SpeciesReportar como inadecuado




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Discrete Dynamics in Nature and Society - Volume 2014 2014, Article ID 548384, 11 pages -

Research Article

School of Science, Shenyang University of Technology, Shenyang 110870, China

Institute of Systems Science, Northeastern University, Shenyang 110819, China

State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China

Received 10 June 2014; Revised 20 October 2014; Accepted 20 October 2014; Published 16 November 2014

Academic Editor: Beatrice Paternoster

Copyright © 2014 Yi 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

The objective of this paper is to study systematically the bifurcation and control of a single-species fish population logistic model with the invasion of alien species based on the theory of singular system and bifurcation. It regards Spartina anglica as an invasive species, which invades the fisheries and aquaculture. Firstly, the stabilities of equilibria in this model are discussed. Moreover, the sufficient conditions for existence of the trans-critical bifurcation and the singularity induced bifurcation are obtained. Secondly, the state feedback controller is designed to eliminate the unexpected singularity induced bifurcation by combining harvested effort with the purification capacity. It obviously inhibits the switch of population and makes the system stable. Finally, the numerical simulation is proposed to show the practical significance of the bifurcation and control from the biological point of view.





Autor: Yi Zhang, Qiaoling Zhang, Jinghao Li, and Qingling Zhang

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



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