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) Zbl 1104.92065 Nonlinear Anal., Real World Appl. 7, No. 5, 1104-1118 (2006). 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. Cited in 163 Documents MSC: 92D40 Ecology 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations 65L99 Numerical methods for ordinary differential equations Keywords:time delay; boundedness; permanence; local stability; global stability; Lyapunov functional PDF BibTeX XML Cite \textit{A. F. Nindjin} et al., Nonlinear Anal., Real World Appl. 7, No. 5, 1104--1118 (2006; Zbl 1104.92065) Full Text: DOI References: [1] Aziz-Alaoui, M. A., Study of Leslie-Gower-type tritrophic population, Chaos Solitons Fractals, 14, 8, 1275-1293 (2002) · Zbl 1031.92027 [2] Aziz-Alaoui, M. A.; Daher Okiye, M., Boundeness and global stability for a predator-prey model with modified Leslie-Gower and Holling-typeII schemes, Appl. Math. Lett., 16, 1069-1075 (2003) · Zbl 1063.34044 [3] Beretta, E.; Kuang, Y., Global analyses in some delayed ratio-depended predator-prey systems, Nonlinear Anal. Theory Methods Appl., 32, 3, 381-408 (1998) · Zbl 0946.34061 [4] Kuang, Y., Delay Differential Equations, with Applications in Population Dynamics (1993), Academic Press: Academic Press New York · Zbl 0777.34002 [5] Upadhyay, R. K.; Rai, V., Crisis-limited chaotic dynamics in ecological systems, Chaos Solitons Fractals, 12, 2, 205-218 (2001) · Zbl 0977.92033 [6] Upadhyay, R. K.; Iyengar, S. R.K., Effect of seasonality on the dynamics of 2 and 3 species prey-predator system, Nonlinear Anal.: Real World Appl., 6, 509-530 (2005) · Zbl 1072.92058 [7] Xu, R.; Chaplain, M. A.J., Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response, Appl. Math. Comput., 130, 441-455 (2002) · Zbl 1030.34069 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.