Phytoplankton–zooplankton dynamics in periodic environments taking into account eutrophication

Luo, Jinhuo

doi:10.1016/j.mbs.2013.06.002

Cited by 37 publications

(15 citation statements)

References 26 publications

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“…where ( ) and ( ) are periodically continuous functions defined on + with the common period > 0. According to the results of [11,17], we obtain the following conclusions.…”

Section: Dynamical Properties Of (3) Without Impulsive Effectmentioning

confidence: 66%

“…where , 10 , , , , , and are positive constants and ( ) is a periodic continuous function on + with the common period > 0. Theorem 4 (see [11]). System (6) is permanent provided that…”

Section: Dynamical Properties Of (3) Without Impulsive Effectmentioning

confidence: 99%

“…Freund et al [4] filled the gap, presenting and discussing simulation results of the seasonally forced Truscott-Brindley model with an exponential function depicting the explosive growth. Later, Luo [11] developed the seasonally forced Truscott-Brindley model by including the growth rate and the intrinsic carrying capacity of phytoplankton changing with respect to time and nutrient concentration. For simplicity we only consider the maximum growth rate in the model (1) as periodically varying function of time due to seasonal variation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics of a Seasonally Forced Phytoplankton-Zooplankton Model with Impulsive Biological Control

Zhao

Yan

2016

Discrete Dynamics in Nature and Society

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This paper investigates the dynamics of a seasonally forced phytoplankton-zooplankton model with impulsive biological control. It shows that the periodic eradicated solution is unstable. Further, the condition for permanence of the system is established by relations between the model parameters and the intensity of the impulses. The numerical analysis is performed to study the effect of seasonality and impulsive perturbations on plankton dynamics. The numerical results imply that the seasonal forcing can trigger more periodic mode and the impulsive period for control of the size of phytoplankton is more practicable to the system than the impulsive release of zooplankton. These conclusions provide a better understanding of controlling harmful algae blooms.

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“…where ( ) and ( ) are periodically continuous functions defined on + with the common period > 0. According to the results of [11,17], we obtain the following conclusions.…”

Section: Dynamical Properties Of (3) Without Impulsive Effectmentioning

confidence: 66%

“…where , 10 , , , , , and are positive constants and ( ) is a periodic continuous function on + with the common period > 0. Theorem 4 (see [11]). System (6) is permanent provided that…”

Section: Dynamical Properties Of (3) Without Impulsive Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of a Seasonally Forced Phytoplankton-Zooplankton Model with Impulsive Biological Control

Zhao

Yan

2016

Discrete Dynamics in Nature and Society

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“…Luo [8] investigated phytoplankton-zooplankton dynamics in periodic environments, where eutrophication was considered. El Saadi and Bah [9] modeled phytoplankton aggregation using numerical treatment and explored the asymptotic behavior of the model.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of a Nutrient-Plankton Model

Wang

Zhao

Dai

et al. 2014

Abstract and Applied Analysis

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We investigated a nonlinear model of the interaction between nutrients and plankton, which was addressed using a pair of reaction-advection-diffusion equations. Based on numerical analysis, we studied a model without diffusion and sinking terms, and we found that the phytoplankton density (a stable state) increased with the increase of nutrient density. We analyzed the model using a linear analysis technique and found that the sinking of phytoplankton could affect the system. If the sinking velocity exceeded a certain critical value, the stable state became unstable and the wavelength of phytoplankton increased with the increase of sinking velocity. Furthermore, band patterns were also produced by our model, which was affected by the diffusion and sinking of phytoplankton. Thus, the change in the diffusion and sinking of phytoplankton led to different spatial distributions of phytoplankton. All of these results are expected to be useful in the study of plankton dynamics in aquatic ecosystems.

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“…Conclusion and discussion. Because of ignoring the time-varying nature of growth rate and environmental biomass of phytoplankton, the traditional autonomous model could not well explain why phytoplankton usually occur in high temperature seasons [28]. In this study, in order to investigate the effect of seasonal temperature on the growth of phytoplankton, by incorporating the time-varying feature of temperature, we propose a new time-dependent bottom-up nutrientphytoplankton interacting model.…”

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confidence: 99%

Effect of seasonal changing temperature on the growth of phytoplankton

Chen¹,

Fan²,

Yuan³

et al. 2017

MBE

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An non-autonomous nutrient-phytoplankton interacting model incorporating the effect of time-varying temperature is established. The impacts of temperature on metabolism of phytoplankton such as nutrient uptake, death rate, and nutrient releasing from particulate nutrient are investigated. The ecological reproductive index is formulated to present a threshold criteria and to characterize the dynamics of phytoplankton. The positive invariance, dissipativity, and the existence and stability of boundary and positive periodic solution are established. The analyses rely on the comparison principle, the coincidence degree theory and Lyapunov direct method. The effect of seasonal temperature and daily temperature on phytoplankton biomass are simulated numerically. Numerical simulation shows that the phytoplankton biomass is very robust to the variation of water temperature. The dynamics of the model and model predictions agree with the experimental data. Our model and analysis provide a possible explanation of triggering mechanism of phytoplankton blooms.

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Phytoplankton–zooplankton dynamics in periodic environments taking into account eutrophication

Cited by 37 publications

References 26 publications

Dynamics of a Seasonally Forced Phytoplankton-Zooplankton Model with Impulsive Biological Control

Dynamics of a Seasonally Forced Phytoplankton-Zooplankton Model with Impulsive Biological Control

Nonlinear Dynamics of a Nutrient-Plankton Model

Effect of seasonal changing temperature on the growth of phytoplankton

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