Plankton nutrient interaction model with effect of toxin in presence of modified traditional Holling Type II functional response

Abstract

A three-dimensional plankton-nutrient interaction model is proposed and analysed which mediated by a toxin-determined functional response. The new functional response is a modification of the traditional Holling Type II functional response by explicitly including a reduction in the consumption of phytoplankton by the zooplankton due to chemical defenses. Our analysis leads to different thresholds in terms of model parameters to find out different steady-states behaviour. It is found that constant nutrient input and dilution rate of nutrient influence the plankton ecosystem model and maintain stability around the coexistent equilibrium. Our observations indicate that if the constant nutrient input crosses a certain critical value, the system enters into Hopf bifurcation. In addition, we have studied the direction of Hopf bifurcation by applying the normal form method. The maximal amount of toxin of phytoplankton species plays a crucial role to change the steady-state behaviour. Computer simulations illustrate the results.

Stability and Hopf Bifurcation in a Three‐Component Planktonic Model with Spatial Diffusion and Time Delay

“…Pal et al [9] further considered the threecomponent model with both nonlinear predation functions by zooplankton. Further, the study was also extended from the perspectives of stochastic dynamics and planktonnutrient interactions, respectively [10,11].…”

Dynamical study of nutrient‐phytoplankton model with toxicity: Effect of diffusion and time delay

“…Chakraborty and Das 16 have obtained the optimal control for a sustainable phytoplankton‐zooplankton system in the presence of toxicity. Beyond the critical value of constant input nutrients, the system shows a Hopf bifurcation in nutrient‐plankton interaction in the presence of toxin 17 . The influence of Allee effect and rate of toxin release in a toxic‐phytoplankton system is investigated by Han and Dai 18 .…”

“…Beyond the critical value of constant input nutrients, the system shows a Hopf bifurcation in nutrient-plankton interaction in the presence of toxin. 17 The influence of Allee effect and rate of toxin release in a toxic-phytoplankton system is investigated by Han and Dai. 18 Ji and Wang 19 have demonstrated a detailed study of stability and bifurcation for a nutrient-phytoplankton system and identified the control parameters of phytoplankton blooms.…”

Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

“…A two zooplankton and one phytoplankton model with toxicity observed that coefficient of toxin plays an important role for existence of Hopf bifurcation around the interior equilibrium [14]. Chatterjee and Pal [15] studied the effect of toxin in nutrient-plankton model and observed that toxic phytoplankton may change the steady-state behavior. De Silva and Jang [16] observed that the mutual interference of zooplankton diminishes harmful blooms.…”