Qualitative Dynamics of a Discrete Phytoplankton-Zooplankton System with Holling Type II Grazing and Type III Toxin Release

2025/07/24 by S. K. Shoyimardonov, Shoyimardonov, Sobirjon
Earth and Planetary Sciences · #Aquatic and Environmental Studies #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2507.18094

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of a discrete phytoplankton-zooplankton model with Holling type~II grazing and Holling type~III toxin release. The existence and stability of positive fixed points are analyzed, and conditions for the occurrence of Neimark--Sacker bifurcation are established. We show how feedback control can suppress complex dynamics near bifurcation. Global stability of the boundary equilibrium is also discussed. Numerical simulations confirm the theoretical findings, illustrating the rich behavior of the model under varying parameters

Citations

• Stability and Bifurcation in a Discrete Phytoplankton-Zooplankton Model with Holling-Type Toxic Effects
• Stability, Bifurcation, and Chaos Control in a Discrete-Time Phytoplankton-Zooplankton Model with Holling Type II and Type III Functional Responses
• Forward hysteresis and Hopf bifurcation in an NPZD model with application to harmful algal blooms
• Neimark-Sacker bifurcation and stability analysis in a discrete phytoplankton-zooplankton system with Holling type II functional response
• Planktons discrete-time dynamical systems
• On ocean ecosystem discrete time dynamics generated by ℓ-Volterra operators
• Toxin-producing Plankton May Act as a Biological Control for Planktonic Blooms—Field Study and Mathematical Modelling

Cited by

• Discrete Dynamics of a Phytoplankton-Zooplankton Model with Toxin-Mediated Interactions

Related

• Discrete Dynamics of a Phytoplankton-Zooplankton Model with Toxin-Mediated Interactions
• Stability and Bifurcation in a Discrete Phytoplankton-Zooplankton Model with Holling-Type Toxic Effects
• Stability, Bifurcation, and Chaos Control in a Discrete-Time Phytoplankton-Zooplankton Model with Holling Type II and Type III Functional Responses
• Neimark-Sacker bifurcation and stability analysis in a discrete phytoplankton-zooplankton system with Holling type II functional response
• Discrete dynamics of phytoplankton-zooplankton systems with Holling type functional responses