Global stability in chemostat-type plankton models with delayed nutrient recycling

He, Xue-Zhong; Ruan, Shigui

doi:10.1007/s002850050128

Cited by 59 publications

(49 citation statements)

References 27 publications

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“…The global stability of the positive equilibrium in the delayed system could possibly be proved with a Lyapunov functional. In He and Ruan (1998), the authors use Lyapunov functionals to provide conditions for global stability in a two-compartment chemostat model that includes a delay in nutrient recycling and in the gestation time.…”

Section: Discussionmentioning

confidence: 99%

“…The length and other characteristic features of the delay can affect stability, and we will analyze this along with the total nutrient in the system. This type of delay has been studied frequently in chemostat-type models, (He and Ruan 1998;Ruan 1998Ruan , 2001. However, the inclusion of delay in a closed system brings forth an alternative structure in the governing equations that requires a different perspective that has received much less attention.…”

Section: Introductionmentioning

confidence: 99%

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A closed NPZ model with delayed nutrient recycling

2013

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We consider a closed Nutrient-Phytoplankton-Zooplankton (NPZ) model that allows for a delay in the nutrient recycling. A delay-dependent conservation law allows us to quantify the total biomass in the system. With this, we can investigate how a planktonic ecosystem is affected by the quantity of biomass it contains and by the properties of the delay distribution. The quantity of biomass and the length of the delay play a significant role in determining the existence of equilibrium solutions, since a sufficiently small amount of biomass or a long enough delay can lead to the extinction of a species. Furthermore, the quantity of biomass and length of delay are important since a small change in either can change the stability of an equilibrium solution. We explore these effects for a variety of delay distributions using both analytical and numerical techniques, and verify these results with simulations.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A closed NPZ model with delayed nutrient recycling

2013

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“…Beretta and Takeuchi [7,8] modelled both of the two delay effects using distributed delay terms and studied the global asymptotic stability of the positive equilibrium by using Lyapunov functionals. See also the works of He et al [9,10] where other related results are proved.…”

Section: Introductionmentioning

confidence: 81%

Spatio-temporal delays in a nutrient-plankton model on a finite domain: linear stability and bifurcations

Gourley

Ruan

2003

Applied Mathematics and Computation

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The issue of how to incorporate time-delays into a mathematical model in which individuals are moving around requires careful consideration. Any time-delay term must also involve a weighted spatial averaging to account for movement of individuals during the time-delay period. Most of the current literature on this subject is on reaction-diffusion equations and concentrates on the simplest case when the spatial domain is infinite. In this paper we consider what changes arise when the domain is finite. Spatial averaging kernels are computed explicitly for the case of a finite, one-dimensional domain. To illustrate the ideas we concentrate on a diffusive nutrient-plankton model. The model is analysed in terms of the local stability of the steady states and bifurcations. The results of some numerical simulations are also presented.

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“…The Lipschitz continuity of the map l m (·) w. r. t. ζ uniformly in y 1 ∈ O 1 provides the inequality (12).…”

Section: −Imentioning

confidence: 99%

Design of a cascade observer for a model of bacterial batch culture with nutrient recycling

Hajji

Rapaport

2010

IFAC Proceedings Volumes

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Global stability in chemostat-type plankton models with delayed nutrient recycling

Cited by 59 publications

References 27 publications

A closed NPZ model with delayed nutrient recycling

A closed NPZ model with delayed nutrient recycling

Spatio-temporal delays in a nutrient-plankton model on a finite domain: linear stability and bifurcations

Design of a cascade observer for a model of bacterial batch culture with nutrient recycling

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