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  • 1Department of Basic Sciences, Yancheng Institute of Technology, Yancheng 224003, China. unfoxeses@yahoo.com.cn

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Time delays in aquatic ecosystems can trigger spatial patterns in competing plankton populations. This study reveals how time lags influence stability and pattern selection in delayed plankton allelopathic systems.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Environmental Science

Background:

  • Spatial patterns are crucial in physical, biological, and social sciences.
  • Time delays are common in aquatic environments due to species maturity and substance production.
  • Understanding the impact of these delays on spatial dynamics is essential.

Purpose of the Study:

  • To investigate how time delays affect the stability and spatial patterns in a delayed plankton allelopathic system.
  • To analyze the relationship between time delays and the emergence of spatial patterns in competing species.
  • To explore the role of time delays in pattern selection.

Main Methods:

  • Analytical stability analysis of the delayed plankton allelopathic system.
  • Numerical simulations using a finite difference scheme.
  • Investigating the effects of varying time delays on system dynamics.

Main Results:

  • Time delay can induce spatial patterns under specific conditions.
  • The delay significantly influences the stability of the plankton system.
  • Numerical simulations demonstrate the critical role of time delay in pattern selection.

Conclusions:

  • Time delays are a key factor in the formation and selection of spatial patterns in plankton communities.
  • The findings provide insights into the complex dynamics of aquatic ecosystems with time-delayed interactions.
  • Further research can explore other environmental factors influencing these spatial dynamics.