Global qualitative analysis of a phytoplankton–zooplankton model in the presence of toxicity

Zhang, Zhenzhen; Rehim, Mehbuba

doi:10.1007/s40435-016-0230-5

Cited by 21 publications

(27 citation statements)

References 30 publications

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“…It can make the unstable system stable by showing its positive impact, whereas it can also be responsible for making the whole system chaotic (Sharma et al. 2014 ; Zhang and Rehim 2017 ). Beretta and Kuang ( 2002 ) have substantially studied the biological models by incorporating the effect of time delay.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Thakur

Srivastava

Ojha

2021

Iran J Sci Technol Trans Sci

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Section: Introductionmentioning

confidence: 99%

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Thakur

Srivastava

Ojha

2021

Iran J Sci Technol Trans Sci

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“…As pointed out in [32], phytoplankton in particular have great contribution for our earth; for example, they furnish food for marine existence and oxygen for human life, and they additionally take in greater than half of carbon dioxide which may be contributing to global warming. Over recent years, many authors have studied phytoplankton-zooplankton models [24,30,[33][34][35][36][37][38][39]. In addition, many other prey-predator models have been developed, and the authors obtained the existence of global Hopf bifurcation in the predator-prey system with delay [40][41][42][43].…”

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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“…In the past decade, the issues of phytoplanktonzooplankton models have been investigated by many experts [2][3][4][5][6][7][8][9][10][11][12][13]. Chattopadhy et al [2] showed the effect of the delay forming the period of toxic substances on blooms.…”

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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Global qualitative analysis of a phytoplankton–zooplankton model in the presence of toxicity

Cited by 21 publications

References 30 publications

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

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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