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Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control

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  • Yapei Wang
  • Min Zhao
  • Xinhong Pan
  • Chuanjun Dai

Abstract

We investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pair of semicontinuous systems with biological and artificial control. First, the existence of an order-1 periodic solution to the system is analyzed using a Poincaré map and a geometric method. The stability conditions of the order-1 periodic solution are obtained by a theoretical mathematical analysis. Furthermore, based on previous analysis, we investigate the bifurcation in the order-1 periodic solution and prove that the order-1 periodic solution breaks up an order-1 periodic solution at least. In addition, the transcritical bifurcation of the system is described. Finally, we provide a series of numerical results that illustrate the feasibility of the theoretical results. Based on the theoretical and numerical results, we analyzed the feasibility of biological and artificial control, which showed that biological and artificial methods can control phytoplankton blooms. These results are expected to be useful for the study of phytoplankton dynamics in aquatic ecosystems.

Suggested Citation

  • Yapei Wang & Min Zhao & Xinhong Pan & Chuanjun Dai, 2014. "Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-15, March.
    • Handle: RePEc:hin:jnddns:914647
    DOI: 10.1155/2014/914647
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    Cited by:

    1. Zhao, Zhong & Luo, Chengguang & Pang, Liuyong & Chen, Ying, 2016. "Nonlinear modelling of the interaction between phytoplankton and zooplankton with the impulsive feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 255-261.

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