A time-delay model for the effect of toxicant in a single species growth with stage-structure
type: Item
instance of: scholarly article
title: A time-delay model for the effect of toxicant in a single species growth with stage-structure
zbMATH Open document ID: 1203.34130
author: Sapna Devi
author: Manju Agarwal
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-07-20T00:00:00Z
review text: The authors investigate a single-species growth model with stage-structure consisting of immature and mature stages for the effects of toxicants with constant maturation time- delay. They study the dynamics of the model in three cases: an instantaneous emission of toxicant, a constant emission of toxicant, and a periodic emission of toxicant into the environment. They present results on positivity and boundedness of all solutions under appropriate conditions. The model equations are analyzed mathematically with regard to the nature of equilibria and their stabilities using the theory of nonlinear differential equations and computer simulations. It is shown that under suitable conditions, there exists a globally asymptotically stable positive equilibrium. It is concluded from the analysis that as the concentration of toxicant in the environment increases, equilibrium densities of both immature and mature populations decrease. It is also noted that the effects of toxicants are more on the equilibrium level of immature population in comparison to the mature population.
reviewed by: Haifeng Huo
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 5757747
zbMATH Keywords: stage-structure
zbMATH Keywords: time-delay
zbMATH Keywords: toxicants
zbMATH Keywords: equilibria
zbMATH Keywords: stability
zbMATH Keywords: periodic perturbation
zbMATH Keywords: numerical simulation
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2009.07.011
OpenAlex ID: W2070352981
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DOI: 10.1016/J.NONRWA.2009.07.011
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description: scientific article; zbMATH DE number 5757747