Nonlinear Dynamics

, Volume 95, Issue 2, pp 875–892 | Cite as

Spatiotemporal dynamics of an NPZ model with prey-taxis and intratrophic predation

  • Evgeniya GirichevaEmail author
Original Paper


Spatiotemporal dynamics of plankton community and the nutrients in a vertical column of water are considered. In this paper, the temporal model is first researched to determine the effect of the density-dependent death rate of predator on the system dynamics. Subsequently, the influence of intraspecific predation is investigated in a spatially distributed model. The effects of this factor and the predator’s search activity on the possibility of spatial pattern formation are also analyzed. Necessary conditions for the Turing and wave instabilities are obtained through local stability analysis around the spatially homogeneous equilibrium. Numerical analysis shows that for an unequal diffusion coefficient, increasing the search activity of zooplankton results in its homogeneous vertical distribution. In addition, increasing the diffusion causes spatial heterogeneity. The stabilizing role of intraspecific predation in the spatial model is obscure. Escalating this factor can also lead to a wave instability. A similar effect on the system stability is provided by taxis in the case of equal diffusion coefficients.


NPZ model Intratrophic predation Prey-taxis Turing and wave instabilities 



This work is supported by the Russian Foundation for Fundamental Research (Grant No. 18-01-00213).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institute of Automation and Control Processes of the FEB RASVladivostokRussia
  2. 2.Far Eastern Federal UniversityVladivostokRussia

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