Spatial dynamics of a nutrient–phytoplankton system with toxic effect on phytoplankton

Chakraborty, Subhendu; Tiwari, Pankaj Kumar; Misra, Arvind; Chattopadhyay, Joydev

doi:10.1016/j.mbs.2015.03.010

Cited by 52 publications

(32 citation statements)

References 31 publications

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“…In 1949, Riley et al [38] first used the mathematical model to study the nutrient-plankton dynamics, which leads to the formulation of a growing number of mathematical models to describe the nutrient-phytoplankton dynamics or nutrient-plankton dynamics, and many dynamic mechanisms of phytoplankton growth response to various factors have been revealed [14,15,22,[39][40][41][42][43][44][45][46][47]. For example, Chen et al [43] showed that the proper control of the ratio for nitrogen and phosphorus can more effectively control and eliminateblue-green algae blooms.…”

Section: Introductionmentioning

confidence: 99%

Impact of Cell Size Effect on Nutrient‐Phytoplankton Dynamics

Liao

Dai

et al. 2019

Complexity

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In this paper, a nutrient-phytoplankton model, which is described by a system of ordinary differential equations incorporating the effect of cell size, and its corresponding stochastic differential equation version are studied analytically and numerically. A key advantage of considering cell size effect is that it can more accurately reveal the intrinsic law of interaction between nutrient and phytoplankton. The main purpose of this paper is to research how cell size affects the nutrient-phytoplankton dynamics within the deterministic and stochastic environments. Mathematically, we show that the existence and stability of the equilibria in the deterministic model can be determined by cell size: the smaller or larger cell size can lead to the disappearance of the positive equilibrium, but the boundary equilibrium always exists and is globally asymptotically stable; the intermediate cell size is capable to drive the positive equilibrium to appear and be globally asymptotically stable, whereas the boundary equilibrium becomes unstable. In the case of the stochastic model, the stochastic dynamics including the stochastic extinction, persistence in the mean, and the existence of ergodic stationary distribution is found to be largely dependent on cell size and noise intensity. Ecologically, via numerical simulations, it is found that the smaller cell size or larger cell size can result in the extinction of phytoplankton, which is similar to the effect of larger random environmental fluctuations on the phytoplankton. More interestingly, it is discovered that the intermediate cell size is the optimal size for promoting the growth of phytoplankton, but increasing appropriately the cell size can rapidly reduce phytoplankton density and nutrient concentrations at the same time, which provides a possible strategy for biological control of algal blooms.

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Section: Introductionmentioning

confidence: 99%

Impact of Cell Size Effect on Nutrient‐Phytoplankton Dynamics

Liao

Dai

et al. 2019

Complexity

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“…However, nutrients play a big role in the growth of plankton. As far as we know, the nutrient-plankton systems have been considered by a number of scholars [24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

A Spatiotemporal Prey-Predator Discrete Model and Optimal Controls for Environmental Sustainability in the Multifishing Areas of Morocco

Bhih

Benfatah

Rhila

et al. 2020

Discrete Dynamics in Nature and Society

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In this work, we propose a multifishing area prey-predator discrete-time model which describes the interaction between the prey and middle and top predators in various areas, which are connected by their movements to their neighbors, to provide realistic description prey effects of two predators. A grid of colored cells is presented to illustrate the entire domain; each cell may represent a subdomain or area. Next, we propose two harvesting control strategies that focus on maximizing the biomass of prey, in the targeted area, and minimizing the biomass of middle and top predators coming from the neighborhood of this targeted area to ensure sustainability and maintain a differential chain system. Theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

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“…The concentration of nutrients can better explain their mechanism in the phytoplankton-zooplankton system. As far as we know, the nutrient-plankton systems have been considered by a number of scholars [14][15][16][17][18][19][20][21]. Chakrabortyour et al [14] demonstrated that the toxin producing phytoplankton (TPP) species control the bloom of other nontoxic phytoplankton species when nutrient-deficient conditions are favorable for TPP species to release toxic chemicals.…”

Section: Introductionmentioning

confidence: 99%

“…Fan et al [16] proposed a nutrient model for a water ecosystem. Chakraborty et al [17] investigated spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton. Wang et al [18] analyzed a nutrient-plankton model with delayed nutrient cycling.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviour of a Nutrient-Plankton Model with Holling Type IV, Delay, and Harvesting

Meng

Jiao-guo

Huo

2018

Discrete Dynamics in Nature and Society

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In this paper, a Holling type IV nutrient-plankton model with time delay and linear plankton harvesting is investigated. The existence and local stability of all equilibria of model without time delay are given. Regarding time delay as bifurcation parameter, such system around the interior equilibrium loses its local stability, and Hopf bifurcation occurs when time delay crosses its critical value. In addition, the properties of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem. What is more, the global continuation of the local Hopf bifurcation is discussed by using a global Hopf bifurcation result. Furthermore, the optimal harvesting is obtained by the Pontryagin's Maximum Principle. Finally, some numerical simulations are given to confirm our theoretical analysis.

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Spatial dynamics of a nutrient–phytoplankton system with toxic effect on phytoplankton

Cited by 52 publications

References 31 publications

Impact of Cell Size Effect on Nutrient‐Phytoplankton Dynamics

Impact of Cell Size Effect on Nutrient‐Phytoplankton Dynamics

A Spatiotemporal Prey-Predator Discrete Model and Optimal Controls for Environmental Sustainability in the Multifishing Areas of Morocco

Dynamical Behaviour of a Nutrient-Plankton Model with Holling Type IV, Delay, and Harvesting

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