Stability, Bifurcation, and Chaos Control in a Discrete-Time Phytoplankton-Zooplankton Model with Holling Type II and Type III Functional Responses

2025/05/15 by S. K. Shoyimardonov, Shoyimardonov, Sobirjon · 3 citations
Medicine · Computer Science · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2505.09954

Abstract

In this paper, we investigate the dynamics of a discrete-time phytoplankton-zooplankton model where the predator functional response and toxin distribution functions follow both Holling Type II and Holling Type III forms simultaneously. We analyze the types of fixed points and the global stability of the system. Additionally, we prove the occurrence of a Neimark-Sacker bifurcation at the positive fixed point. The theoretical findings are validated through numerical simulations

Citations

• 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
• 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
• Qualitative Dynamics of a Discrete Phytoplankton-Zooplankton System with Holling Type II Grazing and Type III Toxin Release
• Stability and Bifurcation Analysis of a Phytoplankton-Zooplankton Model with Linear Functional Responses

Related

• Stability and Bifurcation in a Discrete Phytoplankton-Zooplankton Model with Holling-Type Toxic Effects
• Neimark-Sacker bifurcation and stability analysis in a discrete phytoplankton-zooplankton system with Holling type II functional response
• Qualitative Dynamics of a Discrete Phytoplankton-Zooplankton System with Holling Type II Grazing and Type III Toxin Release
• Discrete Dynamics of a Phytoplankton-Zooplankton Model with Toxin-Mediated Interactions
• Discrete dynamics of phytoplankton-zooplankton systems with Holling type functional responses