Dynamics Analysis of a Nutrient-Plankton Model with a Time Delay

Beibei Wang, Min Zhao, Chuanjun Dai, Hengguo Yu, Nan Wang and Pengfei Wang

Discrete Dynamics in Nature and Society, 2016, vol. 2016, 1-12

Abstract:

We analyze a nutrient-plankton system with a time delay. We choose the time delay as a bifurcation parameter and investigate the stability of a positive equilibrium and the existence of Hopf bifurcations. By using the center manifold theorem and the normal form theory, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are researched. The theoretical results indicate that the time delay can induce a positive equilibrium to switch from a stable to an unstable to a stable state and so on. Numerical simulations show that the theoretical results are correct and feasible, and the system exhibits rich complex dynamics.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:9797624

DOI: 10.1155/2016/9797624

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