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The present investigation deals with a generic oxygen-plankton model with constant time delays using the combinations of analytical and numerical methods. First, a two-component delayed model: the interaction between the concentration of dissolved oxygen and the density of the phytoplankton is examined in terms of the local stability and Hopf bifurcation analysis around the positive steady state. Then, a three-component model (oxygen-phytoplankton-zooplankton system) is investigated. The prime objective of this trio model is to explore how a constant time delay in growth response of phytoplankton and in the gestation time of zooplankton affects the dynamics of interaction between the concentration of oxygen and the density of plankton. The analytical and numerical investigations reveal that the positive steady states for both models are stable in the absence of time delays for a given hypothetical parameter space. Analysing eigenvalues of the characteristic equation which depends on the delay parameters, the conditions for linear stability and the existence of delay-induced Hopf bifurcation threshold are studied for all possible cases. As the delay rate increases, stability of coexistence state switches from stable to unstable. To support the analytical results, detailed numerical simulations are performed. Our findings show that time delay has a significant impact on the dynamics and may provide useful insights into underlying ecological oxygen-plankton interactions.
Aytül Gökçe; Samire Yazar; Yadigar Sekerci. Delay induced nonlinear dynamics of oxygen-plankton interactions. Chaos, Solitons & Fractals 2020, 141, 110327 .
AMA StyleAytül Gökçe, Samire Yazar, Yadigar Sekerci. Delay induced nonlinear dynamics of oxygen-plankton interactions. Chaos, Solitons & Fractals. 2020; 141 ():110327.
Chicago/Turabian StyleAytül Gökçe; Samire Yazar; Yadigar Sekerci. 2020. "Delay induced nonlinear dynamics of oxygen-plankton interactions." Chaos, Solitons & Fractals 141, no. : 110327.
How species and ecosystems respond to the threatened environmental conditions are attracting phenomenon facing ecologists. One can expect species fight against these forces to get rid of extinction, i.e., species tend to adapt genetically or move to a new environment to resilience against extinction. In this paper, this problem is focused theoretically by considering a coupled of the oxygen-plankton model where planktons’ habitat changes and beachhead as a response to climate change. Hence, the dynamics of the oxygen-plankton model is considered assuming the spatial gradient of the growth rate of oxygen, in concern with altered sea surface temperature. It is observed that there exists a relationship between the slope of the gradient and the beachhead at which the oxygen-plankton system can stably survive, which can be defined by a simple function that separates the areas of extinction and persistence. Findings reveal that environmental gradient is an alternative way for species to create a new habitat and sustain the species persistence. Therefore, in this paper, it is shown that, in theory, the recovery of plankton extinction and oxygen depletion under climate change can be achieved by adding a spatial gradient.
Yadigar Sekerci. Climate change forces plankton species to move to get rid of extinction: mathematical modeling approach. The European Physical Journal Plus 2020, 135, 1 -20.
AMA StyleYadigar Sekerci. Climate change forces plankton species to move to get rid of extinction: mathematical modeling approach. The European Physical Journal Plus. 2020; 135 (10):1-20.
Chicago/Turabian StyleYadigar Sekerci. 2020. "Climate change forces plankton species to move to get rid of extinction: mathematical modeling approach." The European Physical Journal Plus 135, no. 10: 1-20.
Yadigar Sekerci. Allee Etkisi Altındaki Av-Avcı Sisteminin Zamana Bağlı Değişimi. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 2020, 7, 54 -65.
AMA StyleYadigar Sekerci. Allee Etkisi Altındaki Av-Avcı Sisteminin Zamana Bağlı Değişimi. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2020; 7 (1):54-65.
Chicago/Turabian StyleYadigar Sekerci. 2020. "Allee Etkisi Altındaki Av-Avcı Sisteminin Zamana Bağlı Değişimi." Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 7, no. 1: 54-65.
Global climate change affects marine species including phytoplankton, which constitute the base of the marine food web, by changing the primary productivity. Global warming affects the ocean surface temperature, in turn leading to a change in the oxygen production of phytoplankton. In this work, the fractional oxygen–phytoplankton–zooplankton mathematical model is considered by the Caputo fractional operator. The production rate of photosynthesis is determined by a temperature function. The model is, therefore, based on the idea that the rate of photosynthesis changes due to the impact of global warming, while phytoplankton oxygen production increases and decreases. We analyze the model with the Caputo fractional derivative differently from the classical case of the model and we compare the results with the integer order derivative when α tends to 1. Existence and uniqueness properties of the oxygen–plankton model have been proved by means of a local Lipschitz condition. It was shown that the species are more sustainable than its corresponding classical case in the Caputo model. Our results show that the effect of global warming on the oxygen production rate has been observed to be quite severe, resulting in oxygen depletion and plankton extinction.Global climate change affects marine species including phytoplankton, which constitute the base of the marine food web, by changing the primary productivity. Global warming affects the ocean surface temperature, in turn leading to a change in the oxygen production of phytoplankton. In this work, the fractional oxygen–phytoplankton–zooplankton mathematical model is considered by the Caputo fractional operator. The production rate of photosynthesis is determined by a temperature function. The model is, therefore, based on the idea that the rate of photosynthesis changes due to the impact of global warming, while phytoplankton oxygen production increases and decreases. We analyze the model with the Caputo fractional derivative differently from the classical case of the model and we compare the results with the integer order derivative when α tends to 1. Existence and uniqueness properties of the oxygen–plankton model have been proved by means of a local Lipschitz condition. It was shown that the species ar...
Ramazan Ozarslan; Yadigar Sekerci. Fractional order oxygen–plankton system under climate change. Chaos: An Interdisciplinary Journal of Nonlinear Science 2020, 30, 033131 .
AMA StyleRamazan Ozarslan, Yadigar Sekerci. Fractional order oxygen–plankton system under climate change. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2020; 30 (3):033131.
Chicago/Turabian StyleRamazan Ozarslan; Yadigar Sekerci. 2020. "Fractional order oxygen–plankton system under climate change." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 3: 033131.
The key issue in ecology is how environmental changes associated with global climate change, specifically rising temperatures influence relationships of species. Predation is one of the main focus for understanding ecosystem responses to climate change. In this work, fractional order prey-predator system is considered by singular and nonsingular fractional operators within Caputo, Caputo–Fabrizio (CF) and Atangana–Baleanu–Caputo (ABC) sense. The predation rate is considered by a function of time, the function of the temperature refer to climate change, which explains how rising temperatures lead to predation. Extensive numerical simulations are performed to provide details of the underlying structure of the system. It is observed that the population fluctuate more in CF model than Caputo and ABC cases in time. Real-world observations are supported by obtained numerical observations of fluctuations in prey and predator populations under the effect of increasing temperature.
Yadigar Sekerci. Climate change effects on fractional order prey-predator model. Chaos, Solitons & Fractals 2020, 134, 109690 .
AMA StyleYadigar Sekerci. Climate change effects on fractional order prey-predator model. Chaos, Solitons & Fractals. 2020; 134 ():109690.
Chicago/Turabian StyleYadigar Sekerci. 2020. "Climate change effects on fractional order prey-predator model." Chaos, Solitons & Fractals 134, no. : 109690.
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.
Yadigar Sekerci; Ramazan Ozarslan. Marine system dynamical response to a changing climate in frame of power law, exponential decay, and Mittag‐Leffler kernel. Mathematical Methods in the Applied Sciences 2020, 43, 5480 -5506.
AMA StyleYadigar Sekerci, Ramazan Ozarslan. Marine system dynamical response to a changing climate in frame of power law, exponential decay, and Mittag‐Leffler kernel. Mathematical Methods in the Applied Sciences. 2020; 43 (8):5480-5506.
Chicago/Turabian StyleYadigar Sekerci; Ramazan Ozarslan. 2020. "Marine system dynamical response to a changing climate in frame of power law, exponential decay, and Mittag‐Leffler kernel." Mathematical Methods in the Applied Sciences 43, no. 8: 5480-5506.
Oxygen production by marine phytoplankton has great importance to reveal the underlying structure of the aquamarine ecosystem. Any change in phytoplankton productivity may influence the marine biodiversity substantially as in fisheries and food supplies; hence, working on plankton is so crucial to detail the ocean biology. In this paper, we study a fractional model for the dynamics of oxygen, phytoplankton and zooplankton within Caputo sense to detail predation effect on oxygen-plankton system. We investigate into this time fractional model by the help of fractional numerical calculations and the parameters are chosen hypothetically in line with the results obtained from classical differential equations. We observe that species distribution and oxygen concentration show similar properties in fractional case while \(\alpha = 1\) with the classical case; it foresees potential oxygen depletion under determined environmental conditions.
Yadigar Sekerci; Ramazan Ozarslan. Dynamic analysis of time fractional order oxygen in a plankton system. The European Physical Journal Plus 2020, 135, 1 -13.
AMA StyleYadigar Sekerci, Ramazan Ozarslan. Dynamic analysis of time fractional order oxygen in a plankton system. The European Physical Journal Plus. 2020; 135 (1):1-13.
Chicago/Turabian StyleYadigar Sekerci; Ramazan Ozarslan. 2020. "Dynamic analysis of time fractional order oxygen in a plankton system." The European Physical Journal Plus 135, no. 1: 1-13.
Yadigar Sekerci. Adaptation of species as response to climate change: Predator-prey mathematical model. AIMS Mathematics 2020, 5, 3875 -3898.
AMA StyleYadigar Sekerci. Adaptation of species as response to climate change: Predator-prey mathematical model. AIMS Mathematics. 2020; 5 (4):3875-3898.
Chicago/Turabian StyleYadigar Sekerci. 2020. "Adaptation of species as response to climate change: Predator-prey mathematical model." AIMS Mathematics 5, no. 4: 3875-3898.
In this work, fractional oxygen-plankton-zooplankton mathematical model with climate change effect is considered by nonsingular fractional operators, Caputo-Fabrizio (CF) and Atangana–Baleanu (ABC). The model is based on the change in oxygen production amount of phytoplankton with the impact of global warming. Global warming influences ocean surface temperature and this case dramatically affects oxygen production of phytoplankton. We analyze the model with nonsingular fractional derivatives differently from integer case of model and we compare results with integer order case, CF and ABC cases. We show that especially ABC fractional model makes the system much more sustainable compared with the integer and CF cases. Our results show that increment of global warming has been observed to be quite effective in the oxygen production rate, resulting in the oxygen depletion and plankton extinction.
Yadigar Sekerci; Ramazan Ozarslan. Oxygen-plankton model under the effect of global warming with nonsingular fractional order. Chaos, Solitons & Fractals 2019, 132, 109532 .
AMA StyleYadigar Sekerci, Ramazan Ozarslan. Oxygen-plankton model under the effect of global warming with nonsingular fractional order. Chaos, Solitons & Fractals. 2019; 132 ():109532.
Chicago/Turabian StyleYadigar Sekerci; Ramazan Ozarslan. 2019. "Oxygen-plankton model under the effect of global warming with nonsingular fractional order." Chaos, Solitons & Fractals 132, no. : 109532.
In this work, we investigate a model of oxygen–phytoplankton–zooplankton dynamics with fractional-order derivatives in different types known as the Caputo–Fabrizio and Atangana–Baleanu derivatives, having nonsingular kernels, exponential and Mittag-Leffler. In order to detail the underlying structure of the oxygen–plankton interaction, the model is detailed in analytical and numerical techniques. Hypothetical set of parameters are used in numerical simulations to guarantee that in natural sense, the system in biologically meaningful region. All results obtained are compared with each other under different parameters, and different fractional orders with simulations.
Yadigar Sekerci; Ramazan Ozarslan. Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives. Physica A: Statistical Mechanics and its Applications 2019, 553, 123942 .
AMA StyleYadigar Sekerci, Ramazan Ozarslan. Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives. Physica A: Statistical Mechanics and its Applications. 2019; 553 ():123942.
Chicago/Turabian StyleYadigar Sekerci; Ramazan Ozarslan. 2019. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives." Physica A: Statistical Mechanics and its Applications 553, no. : 123942.
Decreasing level of dissolved oxygen has recently been reported as a growing ecological problem in seas and oceans around the world. Concentration of oxygen is an important indicator of the marine ecosystem’s health as lack of oxygen (anoxia) can lead to mass mortality of marine fauna. The oxygen decrease is thought to be a result of global warming as warmer water can contain less oxygen. Actual reasons for the observed oxygen decay remain controversial though. Recently, it has been shown that it may as well result from a disruption of phytoplankton photosynthesis. In this paper, we further explore this idea by considering the model of coupled plankton-oxygen dynamics in two spatial dimensions. By means of extensive numerical simulations performed for different initial conditions and in a broad range of parameter values, we show that the system’s dynamics normally lead to the formation of a rich variety of patterns. We reveal how these patterns evolve when the system approaches the tipping point, i.e., the boundary of the safe parameter range beyond which the depletion of oxygen is the only possibility. In particular, we show that close to the tipping point the spatial distribution of the dissolved oxygen tends to become more regular; arguably, this can be considered as an early warning of the approaching catastrophe.
Yadigar Sekerci; Sergei Petrovskii. Pattern Formation in a Model Oxygen-Plankton System. Computation 2018, 6, 59 .
AMA StyleYadigar Sekerci, Sergei Petrovskii. Pattern Formation in a Model Oxygen-Plankton System. Computation. 2018; 6 (4):59.
Chicago/Turabian StyleYadigar Sekerci; Sergei Petrovskii. 2018. "Pattern Formation in a Model Oxygen-Plankton System." Computation 6, no. 4: 59.
We consider the effect of global warming on the coupled plankton-oxygen dynamics in the ocean. The net oxygen production by phytoplankton is known to depend on the water temperature and hence can be disrupted by warming. We address this issue theoretically by considering a mathematical model of the plankton-oxygen system. The model is generic and can account for a variety of biological factors. We first show that sustainable oxygen production by phytoplankton is only possible if the net production rate is above a certain critical value. This result appears to be robust to the details of model parametrization. We then show that, once the effect of zooplankton is taken into account (which consume oxygen and feed on phytoplankton), the plankton-oxygen system can only be stable if the net oxygen production rate is within a certain intermediate range (i.e., not too low and not too high). Correspondingly, we conclude that a sufficiently large increase in the water temperature is likely to push the system out of the safe range, which may result in ocean anoxia and even a global oxygen depletion. We then generalize the model by taking into account the effect of environmental stochasticity and show that, paradoxically, the probability of oxygen depletion may decrease with an increase in the rate of global warming.
Yadigar Sekerci; Sergei Petrovskii. Global Warming Can Lead to Depletion of Oxygen by Disrupting Phytoplankton Photosynthesis: A Mathematical Modelling Approach. Geosciences 2018, 8, 201 .
AMA StyleYadigar Sekerci, Sergei Petrovskii. Global Warming Can Lead to Depletion of Oxygen by Disrupting Phytoplankton Photosynthesis: A Mathematical Modelling Approach. Geosciences. 2018; 8 (6):201.
Chicago/Turabian StyleYadigar Sekerci; Sergei Petrovskii. 2018. "Global Warming Can Lead to Depletion of Oxygen by Disrupting Phytoplankton Photosynthesis: A Mathematical Modelling Approach." Geosciences 8, no. 6: 201.
It is estimated that more than a half of the total atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. Any significant decrease in the net oxygen production by phytoplankton is therefore likely to result in the depletion of atmospheric oxygen and in a global mass mortality of animals and humans. In its turn, the rate of oxygen production is known to depend on water temperature and hence can be affected by the global warming. We address this problem 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, when the temperature rises sufficiently high, a regime shift happens: the sustainable oxygen production becomes impossible and the system's dynamics leads to fast oxygen depletion and plankton extinction. We also consider a scenario when, after a certain period of increase, the temperature is set on a new higher yet apparently safe value, i.e. before the oxygen depletion disaster happens. We show that in this case the system dynamics may exhibit a long-term quasi-sustainable dynamics that can still result in an ecological disaster (oxygen depletion and mass extinctions) but only after a considerable period of time. Finally, we discuss the early warning signals of the approaching regime shift resulting in the disaster.
Sergei Petrovskii; Yadigar Sekerci; Ezio Venturino. Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change. Journal of Theoretical Biology 2017, 424, 91 -109.
AMA StyleSergei Petrovskii, Yadigar Sekerci, Ezio Venturino. Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change. Journal of Theoretical Biology. 2017; 424 ():91-109.
Chicago/Turabian StyleSergei Petrovskii; Yadigar Sekerci; Ezio Venturino. 2017. "Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change." Journal of Theoretical Biology 424, no. : 91-109.
Ocean dynamics is known to have a strong effect on 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.
Yadigar Sekerci; Sergei Petrovskii. Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change. Bulletin of Mathematical Biology 2015, 77, 2325 -2353.
AMA StyleYadigar Sekerci, Sergei Petrovskii. Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change. Bulletin of Mathematical Biology. 2015; 77 (12):2325-2353.
Chicago/Turabian StyleYadigar Sekerci; Sergei Petrovskii. 2015. "Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change." Bulletin of Mathematical Biology 77, no. 12: 2325-2353.
Oxygen production due to phytoplankton photosynthesis is a crucial phenomenon underlying the dynamics of marine ecosystems. However, most of the existing literature focus on other aspects of the plankton community functioning, thus leaving the issue of the coupled oxygen-plankton dynamics understudied. In this paper, we consider a generic model of the oxygen-phytoplankton-zooplankton dynamics to make an insight into the basic properties of the plankton-oxygen interactions. The model is analyzed both analytically and numerically. We first consider the nonspatial model and show that it predicts possible oxygen depletion under certain environmental conditions. We then consider the spatially explicit model and show that it exhibits a rich variety of spatiotemporal patterns including travelling fronts of oxygen depletion, dynamical stabilization of unstable equilibrium and spatiotemporal chaos.
Yadigar Sekerci; Sergei Petrovskii. Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System. Mathematical Modelling of Natural Phenomena 2015, 10, 96 -114.
AMA StyleYadigar Sekerci, Sergei Petrovskii. Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System. Mathematical Modelling of Natural Phenomena. 2015; 10 (2):96-114.
Chicago/Turabian StyleYadigar Sekerci; Sergei Petrovskii. 2015. "Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System." Mathematical Modelling of Natural Phenomena 10, no. 2: 96-114.