Dynamical analysis of toxin producing Phytoplankton–Zooplankton interactions

Saha, Tapan Kumar; Bandyopadhyay, Malay

doi:10.1016/j.nonrwa.2007.09.001

Cited by 117 publications

(84 citation statements)

References 14 publications

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“…Let 1 stand for the time delay in conversion of food to viable biomass for the species, and 2 is the discrete time period required for the maturity of phytoplankton cells to liberate toxic substances. Based on model 3 in [5], we intend to study a model system with the assumption that ( ) and ( ) are described by same type of function, namely, Tissiet functional response. Then we arrive at the following model:…”

Section: State Of the Modelmentioning

confidence: 99%

“…In [5,10,[28][29][30][31], the following plausible toxic-phytoplankton-zooplankton system has been studied:…”

Section: Introductionmentioning

confidence: 99%

“…Model (1) has been studied for the following cases: (1) when ( ) is linear but ( ) is Holling type II [10,28,29] or Holling type III [10]; (2) when ( ) and ( ) are both Holling type II [5,10] or Holling type III [10]; (3) when ( ) is Holling type II while ( ) is Holling type III [10].…”

Section: Introductionmentioning

confidence: 99%

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On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay

Rehim

Muhammadhaji

2015

Discrete Dynamics in Nature and Society

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A toxin producing phytoplankton-zooplankton model with inhibitory exponential substrate and time delay has been formulated and analyzed. Since the liberation of toxic substances by phytoplankton species is not an instantaneous process but is mediated by some time lag required for maturity of the species and the zooplankton mortality due to the toxic phytoplankton bloom occurs after some time laps of the bloom of toxic phytoplankton, we induced a discrete time delay to both of the consume response function and distribution of toxic substance term. Furthermore, based on the fact that the predation rate decreases at large toxicphytoplankton density, the system is modelled via a Tissiet type functional response. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.

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Section: State Of the Modelmentioning

confidence: 99%

“…In [5,10,[28][29][30][31], the following plausible toxic-phytoplankton-zooplankton system has been studied:…”

Section: Introductionmentioning

confidence: 99%

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On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay

Rehim

Muhammadhaji

2015

Discrete Dynamics in Nature and Society

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“…The NPZ model incorporates one of the simplest sets of dynamics that usefully describe oceanic plankton dynamics [1]. Phytoplankton-zooplankton models have been studied by many authors [2][3][4][5][6][7][8][9][10]. Some type of phytoplankton produce toxin as a defensive strategy against the predation by zooplankton, these types are known as toxic phytoplankton.…”

Section: Introductionmentioning

confidence: 99%

“…Roy [4] has constructed a mathematical model for describing the interaction between a nontoxic and a toxic phytoplankton under a single nutrient. Saha and Bandyopadhyay [5] considered a toxin producing phytoplanktonzooplankton model. Since the phytoplankton is a base of all the aquatic food chain and food web systems and most of zooplankton organism depends directly on the phytoplankton in its feeding process.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of nutrient, toxic phytoplankton, nontoxic phytoplankton and zooplankton model

Hussien

Naji²,

Majeed³

2016

IJAMR

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The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation and Hopf bifurcation are investigated. Finally, numerical simulation is used to study the global dynamics of this model.

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Dynamical behavior of systems of two phytoplankton and one zooplankton populations with toxin producing phytoplankton

Silva

Jang

2017

Math Methods in App Sciences

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Three-compartment mathematical models of non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP), and zooplankton are proposed to explore the role of TPP in algal blooms. The mutual interference between predator zooplankton and avoidance of TPP by zooplankton are incorporated into the model. The NTP and TPP engage in exploit competition and the toxin produced by TPP has no effect on NTP. Using the concept of uniform persistence, we establish coexistence of NTP, TPP, and zooplankton in certain parameter regimes. We study the effects of mutual interference and avoidance by zooplankton upon the population interactions. In addition to the toxin producing mechanism, it is concluded that mutual interference of zooplankton is an important factor for diminishing harmful blooms.

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Dynamical analysis of toxin producing Phytoplankton–Zooplankton interactions

Cited by 117 publications

References 14 publications

On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay

On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay

The dynamics of nutrient, toxic phytoplankton, nontoxic phytoplankton and zooplankton model

Dynamical behavior of systems of two phytoplankton and one zooplankton populations with toxin producing phytoplankton

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