<p>This paper investigates the stochastic dynamics and impulsive control strategies for a toxin-producing phytoplankton-zooplankton system with nutrients enrichment and additional food provision to zooplankton. First, we formulate a novel stochastic phytoplankton-zooplankton system that integrates phytoplankton toxicity, nutrients enrichment, and additional food. Using mathematical analysis, we systematically derive conditions for the global existence, uniqueness, boundedness, persistence, and extinction of the system. We further prove the existence of a unique stationary distribution, indicating that plankton populations can persist for a long time. To mitigate system perturbations induced by multifactor disturbances, we propose a practically implementable impulsive control framework. Our numerical results reveal that plankton persistence and extinction are sensitive to fluctuations in nutrient availability. Notably, plankton extinction is possible in a system subjected to high-intensity stochastic disturbances, but zooplankton can facilitate population survival in such a system when provided with additional food. Furthermore, increased phytoplankton toxicity disrupts population balance, but targeted impulsive control schemes (involving control strength and period) can steer the system toward a desired ecological state. These findings elucidate the complex stochastic dynamics of plankton populations under multifactor perturbations, providing actionable insights to maintain the development of aquatic ecosystems.</p>

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Dynamics and impulsive control of a stochastic toxin-producing phytoplankton-zooplankton system with nutrient enrichment and additional food

  • He Liu,
  • Chuanjun Dai,
  • Hengguo Yu,
  • Qing Guo,
  • Yi Wang,
  • Long Guo,
  • Min Zhao

摘要

This paper investigates the stochastic dynamics and impulsive control strategies for a toxin-producing phytoplankton-zooplankton system with nutrients enrichment and additional food provision to zooplankton. First, we formulate a novel stochastic phytoplankton-zooplankton system that integrates phytoplankton toxicity, nutrients enrichment, and additional food. Using mathematical analysis, we systematically derive conditions for the global existence, uniqueness, boundedness, persistence, and extinction of the system. We further prove the existence of a unique stationary distribution, indicating that plankton populations can persist for a long time. To mitigate system perturbations induced by multifactor disturbances, we propose a practically implementable impulsive control framework. Our numerical results reveal that plankton persistence and extinction are sensitive to fluctuations in nutrient availability. Notably, plankton extinction is possible in a system subjected to high-intensity stochastic disturbances, but zooplankton can facilitate population survival in such a system when provided with additional food. Furthermore, increased phytoplankton toxicity disrupts population balance, but targeted impulsive control schemes (involving control strength and period) can steer the system toward a desired ecological state. These findings elucidate the complex stochastic dynamics of plankton populations under multifactor perturbations, providing actionable insights to maintain the development of aquatic ecosystems.