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Dynamical Behaviour of a Nutrient-Plankton Model with Holling Type IV, Delay, and Harvesting

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  • Xin-You Meng
  • Jiao-Guo Wang
  • Hai-Feng Huo

Abstract

In this paper, a Holling type IV nutrient-plankton model with time delay and linear plankton harvesting is investigated. The existence and local stability of all equilibria of model without time delay are given. Regarding time delay as bifurcation parameter, such system around the interior equilibrium loses its local stability, and Hopf bifurcation occurs when time delay crosses its critical value. In addition, the properties of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem. What is more, the global continuation of the local Hopf bifurcation is discussed by using a global Hopf bifurcation result. Furthermore, the optimal harvesting is obtained by the Pontryagin’s Maximum Principle. Finally, some numerical simulations are given to confirm our theoretical analysis.

Suggested Citation

  • Xin-You Meng & Jiao-Guo Wang & Hai-Feng Huo, 2018. "Dynamical Behaviour of a Nutrient-Plankton Model with Holling Type IV, Delay, and Harvesting," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-19, December.
    • Handle: RePEc:hin:jnddns:9232590
    DOI: 10.1155/2018/9232590
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    Cited by:

    1. Thakur, Nilesh Kumar & Ojha, Archana & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2021. "An investigation of delay induced stability transition in nutrient-plankton systems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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