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Zbl 1104.92065
Nindjin, A.F.; Aziz-Alaoui, M.A.; Cadivel, M.
Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay. (English)
[J] Nonlinear Anal., Real World Appl. 7, No. 5, 1104-1118 (2006). ISSN 1468-1218

Summary: A two-dimensional delayed continuous-time dynamical system modeling a predator-prey food chain, and based on a modified version of Holling type-II scheme, is investigated. By constructing a Lyapunov function, we obtain a sufficient condition for global stability of the positive equilibrium. We also present some related qualitative results for this system.

MSC 2000:: *92D40 Ecology
34D20 Lyapunov stability of ODE
34D23 Global stability
65L99 Numerical methods for ODE

Keywords: time delay; boundedness; permanence; local stability; global stability; Lyapunov functional

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Zentralblatt MATH Berlin [Germany]