Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System

Sekerci, Yadigar; Petrovskii, Sergei

doi:10.1051/mmnp/201510207

Cited by 27 publications

(19 citation statements)

References 31 publications

(24 reference statements)

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“…Dynamics of the dissolved oxygen in marine ecosystems has been a focus on increasing attention recently [2,8,10,42,43,58,75] as the concentration of dissolved oxygen is one of the fundamental environmental variables defining the well-being of a marine ecosystem. A decrease in the oxygen concentration below a certain level can results in hypoxia and mass mortality of marine fauna because of asphyxiation.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change

2015

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Abstract. Ocean dynamics is known to have a strong effect the global climate change and on the composition of the atmosphere. In particular, it is estimated that about 70% of the atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. However, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. In this paper, we address this issue theoretically by considering a model of a coupled plankton-oxygen dynamics where the rate of oxygen production slowly changes with time to account for the ocean warming. We show that a sustainable oxygen production is only possible in an intermediate range of the production rate. If, in the course of time, the oxygen production rate becomes too low or too high, the system's dynamics changes abruptly resulting in the oxygen depletion and plankton extinction. Our results indicate that the depletion of atmospheric oxygen on global scale (which, if happens, obviously can kill most of life on Earth) is another possible catastrophic consequence of the global warming, a global ecological disaster that has been overlooked.

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Section: Discussionmentioning

confidence: 99%

Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change

2015

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“…Furthermore, some studies about integer‐order phytoplankton‐zooplankton interactions can be found in other works and oxygen‐plankton interactions in other studies . We can mention some studies on fractional derivatives on the applications of plankton dynamical systems Eze and Oyesanya, and so on .…”

Section: Introductionmentioning

confidence: 99%

“…The fundamental information for the fractional model is given in Section . The integer‐order oxygen‐plankton model and its fractional form is described under the Caputo, ABC, and CF fractional derivatives in Section . In Section , the existence and uniqueness of the system is detailed.…”

Section: Introductionmentioning

confidence: 99%

Marine system dynamical response to a changing climate in frame of power law, exponential decay, and Mittag‐Leffler kernel

Sekerci

Özarslan

2020

Math Methods in App Sciences

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The increase of sea surface temperature in ocean changes the photosynthetic production rate of phytoplankton. Therefore, it is crucial to understand the relation between temperature and phytoplanktons photosynthesis to deal the extinction caused by excessive increase in temperature. It is worth observing that temperature is one of the most principal limiting factors for phytoplanktons production due to photosynthetic enzymes work at their optimum temperature levels. In this study, the fractional oxygen-phytoplankton-zooplankton model is considered by singular and nonsingular fractional operators within Caputo, Caputo-Fabrizio, and Atangana-Baleanu in Caputo sense. The rate of oxygen production is considered by a function of temperature account for the sea surface warming. At first, the temperature function is constant and then it starts to increase, after a certain time of increase, before the oxygen depletion begins, the temperature is set to a higher secure value. With this temperature function choice, detailed numerical simulations are carried out to provide details of the internal structure of the system. We observe that the species are more sustainable in Caputo model than its corresponding integer-order model. KEYWORDSCaputo, existence and uniqueness, global warming, nonsingular fractional derivatives, oxygen-plankton system, piece-wise function MSC CLASSIFICATION26A33; 37N25; 92B05; 97M60

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“…In this issue, three contributions [2,4,20] directly focus on the role of space in population dynamics.…”

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confidence: 99%

“…In their study, Y. Sekerci and S. Petrovskii [20] explore how the dynamics of marine planktonic ecosystems are influenced by oxygen production due to photosynthetic activity of phytoplankton. This is a novel approach to modelling plankton communities since most of the existing literature complectly ignores the oxygen-plankton interactions.…”

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confidence: 99%

Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue

Морозов

2015

Math. Model. Nat. Phenom.

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Mathematical modelling in ecology, epidemiology and eco-epidemiology is a vast and constantly growing research field. This is perhaps unsurprising since mathematical models can provide a wide-ranging exploration of the biological problem without a need for experiments which are usually expensive and can be potentially dangerous to ecosystems. The current Special Issue of MMNP presents recent findings and developments in the following areas of theoretical ecology and epidemiology: (i) revealing the biological processes behind observed complex patterns; (iii) modelling the role of dispersal and spatial heterogeneity in species persistence; (ii) applications of bifurcation theory in population dynamics and epidemiology; (iv) the role of selection in self-replicating biological and ecological systems; (v) sensitivity, predictability and control of biological models in a noisy environment. It is important to emphasize that many of the contributions to this issue are not limited to one of the above topics, but rather lie at the interface of several of them.The work of D. Ahmed and S. Petrovskii [1] studies the movement of insects whose spatial dispersal is a random variable and is described by a certain probability distribution. Understanding the mechanisms of insects movement behaviour is a highly relevant problem from the practical point of view, since it can help us to correctly interpret the results of insect trapping, which is the basis of many current pest monitoring programs [17]. There is a lively ongoing debate in the literature regarding the possibility of Lévy-type movement behaviour by animals, as opposed to the Brownian motion, and various mechanisms have been proposed to explain the observed patterns [3,16,24]. Ahmed and Petrovskii provide an alternative description of Levy-type movement by introducing time-dependent diffusivity. In particular, the authors claim that the trap counts of insects whose dynamics is given by an example of a Lévy-type distribution -a Cauchy type random walk -can be successfully modelled via a different movement pattern: classical Brownian motion with a time-dependent diffusion coefficient. Thus, the authors provide an excellent example of how two completely different mechanisms can describe the same pattern of field observations.Among the central topics in theoretical ecology is the understanding of the role of space in population dynamics and species persistence across different time scales [6,7,11,12]. In this issue, three contributions [2,4,20] directly focus on the role of space in population dynamics.Modelling the mechanisms of biological aggregation and patchiness is a pertinent topic in theoretical ecology, with various models suggested [6,14,19]. In their work, R. Eftimie and A. Coulier [4] explore the effects of communication between organisms on the formation and structure of large biological agc EDP Sciences, 2015 Article published by EDP Sciences and available at

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Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System

Cited by 27 publications

References 31 publications

Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change

Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change

Marine system dynamical response to a changing climate in frame of power law, exponential decay, and Mittag‐Leffler kernel

Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue

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