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A Lyapunov functional for a stage-structured predator-prey model with nonlinear predation rate
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Mathematics, Jiangsu University, ZhenJiang, Jiangsu, PR China.
2010 (English)In: Nonlinear Analysis, ISSN 1468-1218, Vol. 11, no 5, 3653-3665 p.Article in journal (Refereed) Published
Abstract [en]

We consider the dynamics of a general stage-structured predator-prey model which generalizes several known predator-prey, SEIR, and virus dynamics models, assuming that the intrinsic growth rate of the prey, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for the local stability of the equilibria together with estimations of their respective domains of attraction, while observing that in several particular but important situations these conditions yield global stability results. The biological significance of these conditions is discussed and the existence of the positive steady state is also investigated.

Place, publisher, year, edition, pages
Elsevier, 2010. Vol. 11, no 5, 3653-3665 p.
Keyword [en]
Lyapunov functional, Predator-prey model, Stage structure, Nonlinear predation rate, Stability
National Category
URN: urn:nbn:se:umu:diva-109739DOI: 10.1016/j.nonrwa.2010.01.012ISI: 000281390000033OAI: diva2:859010
Available from: 2015-10-05 Created: 2015-10-05 Last updated: 2015-10-05Bibliographically approved

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Zhang, Hong
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Department of Mathematics and Mathematical Statistics
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