zbMATH — the first resource for mathematics

The qualitative analysis of \(N\)-species nonlinear prey-competition systems. (English) Zbl 1045.92038
Summary: We consider an \(N\)-species nonlinear prey-competition system. Using a differential inequality theorem and the \(V\)-function method, we obtain some sufficient conditions for permanence and global asymptotic stability of the system.

92D25 Population dynamics (general)
34D23 Global stability of solutions to ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
34D05 Asymptotic properties of solutions to ordinary differential equations
37N25 Dynamical systems in biology
Full Text: DOI
[1] Li, C.; Lu, S., The qualitative analysis of N-species periodic coefficient, nonlinear relation, prey – competition systems, Appl. math. J. Chinese univ. series A, 12, 2, 147-156, (1997) · Zbl 0880.34042
[2] Gopalsamy, K., Exchange of equilibria in two species lotka – volterra competition models, J. austral. math. soc. (series B), 24, 160-170, (1982) · Zbl 0498.92016
[3] Gopalsamy, K., Global asymptotic stability in a periodic lotka – volterra system, J. austral. math. soc. (series B), 27, 66-72, (1985) · Zbl 0588.92019
[4] Zhao, X.-Q., The qualitative analysis of n-species lotka – volterra periodic competition systems, Math. comput. modelling, 15, 11, 3-8, (1991) · Zbl 0756.34048
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.