Модельная Оценка Биомассы Фитопланктона Оз. Иссык-Куль По Данным Дистанционного Зондирования

Abakumov, A.I.; Pak, Soojong; Morozov, M. A.; Тыныбеков, А. К.

doi:10.1134/s0320965219060020

Cited by 2 publications

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“…Традиционно данные появлялись из анализа образцов, взятых с борта судов, находящихся в море, что позволяло получить лишь нерегулярные и существенно неоднородные оценки его обилия. В последнее время появилась возможность использовать спутниковые наблюдения, при этом идентификация и интерпретация той части спектра излучения, которая связана с планктоном, остается чрезвычайно сложной задачей [напр., [8][9][10][11][12][13][14]. Поэтому теоретическое моделирование динамики обилия планктона необходимо для понимания физических процессов, влияющих на его динамику и последствия ее изменения для океанов и атмосферы.…”

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Discrete-Time Model of Seasonal Plankton Bloom

Неверова¹,

Zhdanova²,

Abakumov³

2020

Math.Biol.Bioinf.

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The most interesting results in modeling phytoplankton bloom were obtained based on a modification of the classical system of phytoplankton and zooplankton interaction. The modifications using delayed equations, as well as piecewise continuous functions with a delayed response to intoxication processes, made it possible to obtain adequate phytoplankton dynamics like in nature. This work develops a dynamic model of phytoplankton-zooplankton community consisting of two equations with discrete time. We use recurrent equations, which allows to describe delay in response naturally. The proposed model takes into account the phytoplankton toxicity and zooplankton response associated with phytoplankton toxicity. We use a discrete analogue of the Verhulst model to describe the dynamics of each of the species in the community under autoregulation processes. We use Holling-II type response function taking into account predator saturation to describe decrease in phytoplankton density due to its consumption by zooplankton. Growth and survival rates of zooplankton also depend on its feeding. Zooplankton mortality, caused by an increase in the toxic substances concentration with high density of zooplankton, is included in the limiting processes. An analytical and numerical study of the model proposed is made. The analysis shows that the stability loss of nontrivial fixed point corresponding to the coexistence of phytoplankton and zooplankton can occur through a cascade of period doubling bifurcations and according to the Neimark-Saker scenario leading to the appearance of quasiperiodic fluctuations as well. The proposed dynamic model of the phytoplankton and zooplankton community allows observing long-period oscillations, which is consistent with the results of field experiments. As well, the model have multistability areas, where a variation in initial conditions with the unchanged values of all model parameters can result in a shift of the current dynamic mode.

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Discrete-Time Model of Seasonal Plankton Bloom

Неверова¹,

Zhdanova²,

Abakumov³

2020

Math.Biol.Bioinf.

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“…Использование систем уравнений с дискретным временем позволяет учитывать этот суточный ритм. Большинство натурных наблюдений и замеров, собираемых в ходе изучения планктонных сообществ, также имеют суточный шаг [напр., [17][18][19]. Дополнительной аргументацией в пользу применения моделей с дискретным временем является то, что они позволяют описывать эффекты запаздывания естественным образом [20][21][22].…”

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Comparative Dynamics Analysis of Simple Mathematical Models of the Plankton Communities Considering Various Types of Response Function

Neverova¹,

Zhdanova²

2022

Math.Biol.Bioinf.

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The paper proposes a two-component discrete-time model of the plankton community, taking into account features of the development and interaction of phytoplankton and zooplankton. To describe the interaction between these species and to compare the system dynamics, we use the following set of response functions: type II and III Holling function and the Arditi–Ginzburg response function, each of which describes trophic interactions between phytoplankton and zooplankton. An analytical and numerical study of the model proposed is made. The analysis shows that the variation of trophic functions does not change the dynamic behavior of the model fundamentally. The stability loss of nontrivial fixed point corresponding to the coexistence of phytoplankton and zooplankton can occur through a cascade of period-doubling bifurcations and according to the Neimark–Saker scenario, which allows us to observe the appearance of long-period oscillations representing the alternation of peaks and reduction in the number of species as a result of the predator-prey interaction. As well, the model has multistability areas, where a variation in initial conditions with the unchanged values of all model parameters can result in a shift of the current dynamic mode. Each of the models is shown to demonstrate conditional coexistence when a variation of the current community structure can lead to the extinction of the entire community or its part. Considering the characteristics of the species composition, the model with the type II Holling function seems a more suitable for describing the dynamics of the plankton community. Such a system is consistent with the idea that phytoplankton is a fast variable and predator dynamics is slow; thus, long-period fluctuations occur at high phytoplankton growth rates and low zooplankton ones. The model with the Arditi–Ginzburg functional response demonstrates quasi-periodic fluctuations in a narrow parametric aria with a high predator growth rate and low prey growth rate. The quasi-periodic dynamics regions in the model with the Holling type III functional response correspond to the conception of fast and slow variables, however in this case, the stability of the system increases, and the Neimark-Sacker bifurcation occurs even at a higher growth rate of zooplankton.

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Модельная Оценка Биомассы Фитопланктона Оз. Иссык-Куль По Данным Дистанционного Зондирования

Cited by 2 publications

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Discrete-Time Model of Seasonal Plankton Bloom

Discrete-Time Model of Seasonal Plankton Bloom

Comparative Dynamics Analysis of Simple Mathematical Models of the Plankton Communities Considering Various Types of Response Function

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