A Lyapunov functional for a stage-structured predator-prey model with nonlinear predation rate
2010 (English)In: Nonlinear Analysis, ISSN 1468-1218, Vol. 11, no 5, 3653-3665 p.Article in journal (Refereed) Published
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.
Lyapunov functional, Predator-prey model, Stage structure, Nonlinear predation rate, Stability
IdentifiersURN: urn:nbn:se:umu:diva-109739DOI: 10.1016/j.nonrwa.2010.01.012ISI: 000281390000033OAI: oai:DiVA.org:umu-109739DiVA: diva2:859010