×

Permanence in nonautonomous predator-prey Lotka-Volterra systems. (English) Zbl 1054.34080

A two species Lotka-Volterra predator-prey system is considered. It is assumed that the coefficients are nonautonomous, continuous, and bounded functions. By estimating the bounds of the solutions, sufficient conditions are obtained for the system to be permanent. The case with periodic coefficients is also briefly discussed.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ding, T., Huang, H., Zanolin, F. A priori bounds and periodic solutions for a class of planar systems with applications to Lotka-Volterra equations. Discrete and Continuous Dynamical Systems, 1: 103–117 (1995) · Zbl 0877.34035
[2] Lopez-Gomez, J., Ortega, R., Tineo, A. The periodic predator-prey Lotka-Volterra model. Advances in Differential Equations, 1: 403–423 (1996) · Zbl 0849.34026
[3] Ma, Z., Wang, W. Asymptotic behavior of predator-prey system with time dependent coefficient. Appl. Anal., 34: 79–90 (1989) · Zbl 0658.34044
[4] Teng, Z. Some new results of two dimensional periodic lotka-volterra systems. Acta Math. Scientia., 18(2): 168–175 (1998) (in Chinese) · Zbl 0913.34038
[5] Teng, Z., Chen, L. Necessary and sufficient conditions for existence of positive periodic solutions of periodic predator-prey systems. Acta Math. Scientia., 18(4): 402–406 (1998) (in Chinese) · Zbl 0914.92019
[6] Teng, Z., Yu, Y. The extinction in nonautonomous prey-predator Lotka-Volterra systems. Acta Math. Appl. Sinica, 15(4): 401–408 (1999) · Zbl 1007.92031
[7] Teng, Z., Yu, Y., Feng, B. The stability of positive periodic solution for periodic predator-prey systems. Acta Math. Appl. Sinica, 21(4): 589–596 (1998) (in Chinese) · Zbl 0961.92027
[8] Tineo, A. An lterative scheme for the N-competing species problem. J. Diff. Equs., 116: 1–15 (1995) · Zbl 0823.34048
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.