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Taxis-driven complex patterns of a plankton model.

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Repulsive phytoplankton-taxis, not self-diffusion, can induce Turing patterns in zooplankton-phytoplankton models. This study reveals taxis

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Area of Science:

  • Ecological modeling
  • Pattern formation dynamics
  • Mathematical biology

Background:

  • Turing patterns are typically induced by diffusion-driven instability.
  • Self-diffusion is often considered a prerequisite for pattern formation.
  • Zooplankton-phytoplankton interactions are crucial in marine ecosystems.

Purpose of the Study:

  • To investigate pattern formation in a zooplankton-phytoplankton model with phytoplankton-taxis.
  • To determine if taxis can induce Turing patterns without self-diffusion.
  • To analyze the role of attractive versus repulsive phytoplankton-taxis.

Main Methods:

  • Mathematical modeling of zooplankton-phytoplankton dynamics.
  • Analysis of Turing instability using the phytoplankton-taxis sensitivity coefficient.
  • Numerical simulations in various spatial domains (1D, 2D, spherical, zebra surfaces).

Main Results:

  • Turing instability is induced only by repulsive phytoplankton-taxis.
  • Attractive phytoplankton-taxis does not induce Turing instability.
  • The system lacks Turing instability when phytoplankton-taxis is absent.
  • Complex patterns were observed in diverse numerical simulations.

Conclusions:

  • Phytoplankton-taxis, particularly repulsive interactions, is pivotal for Turing pattern formation.
  • Self-diffusion is not essential for inducing Turing patterns in this model.
  • The findings enhance understanding of predator-prey dynamics and pattern emergence.