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A coupled plankton system with instantaneous and delayed predation.

Yuan Yuan1

  • 1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada, A1C 5S7. yyuan@mun.ca

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|August 10, 2012
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Summary

This study introduces two plankton population models, one with immediate and one with delayed predation. Analyzing these models reveals conditions for species coexistence and stability under varying fish densities and maturation delays.

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Area of Science:

  • Ecological modeling
  • Population dynamics
  • Mathematical biology

Background:

  • Plankton populations are crucial to aquatic ecosystems.
  • Predation dynamics significantly influence species coexistence.
  • Time delays in ecological interactions can alter population stability.

Purpose of the Study:

  • To introduce and analyze two plankton population models: one with instantaneous predation and one with delayed predation.
  • To investigate the conditions required for the coexistence of phytoplankton and zooplankton.
  • To examine the impact of fish predation and maturation time delays on population stability and bifurcation.

Main Methods:

  • Development of two coupled differential equation models.
  • Analytical investigation of dynamical behavior.
  • Numerical simulations to explore stability and bifurcation.

Main Results:

  • Identification of conditions for stable coexistence of phytoplankton and zooplankton.
  • Analysis of how fish density affects population dynamics.
  • Demonstration of the influence of maturation time delays on model stability.

Conclusions:

  • The presence and timing of predation, particularly by fish, critically affect plankton population dynamics and coexistence.
  • Maturation time delays can lead to complex dynamical behaviors, including bifurcations.
  • These models provide a framework for understanding predator-prey interactions in aquatic ecosystems.