Displaying similar documents to “Modeling the role of constant and time varying recycling delay on an ecological food chain”

Stability switches for some class of delayed population models

Joanna Skonieczna, Urszula Foryś (2011)

Applicationes Mathematicae

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We study stability switches for some class of delay differential equations with one discrete delay. We describe and use a simple method of checking the change of stability which originally comes from the paper of Cook and Driessche (1986). We explain this method on the examples of three types of prey-predator models with delay and compare the dynamics of these models under increasing delay.

Delays induced in population dynamics

Eva Sánchez (2003)

Banach Center Publications

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This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to examine how the delays emerge from inner mechanisms in the model, how they induce oscillations and stability switches in the system and how the qualitative behaviour of a biological model depends on the form of the delay.

Usefulness of Biocontrol of Pests in Tea: A Mathematical Model

A. Maiti, A. K. Pal, G. P. Samanta (2008)

Mathematical Modelling of Natural Phenomena

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Nowadays there has been a growing consciousness among the tea industry to reduce the use of the chemical pesticides for pest control. Predators are beneficial insects that feed on harmful insects and mites, which incur considerable loss of production of tea. In this paper we have considered a tritrophic model consisting of tea plant, pest and predator to analyze different field observations. The effect of discrete time-delay on the tritrophic model is studied critically. The dynamical...

Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, Mikhail Kolev (2003)

Banach Center Publications

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The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties...

An epidemic model with a time delay in transmission

Q. J. A. Khan, E. V. Krishnan (2003)

Applications of Mathematics

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We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.

Logistic equations in tumour growth modelling

Urszula Foryś, Anna Marciniak-Czochra (2003)

International Journal of Applied Mathematics and Computer Science

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The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are...