论文信息 - Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model

Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model

The discrete Leslie-Gower predator-prey model is studied. The model allows for afluctuating environment. Sufficient conditions which guarantee the permanence of the model are obtained at first, assuming that the coefficients in the model are periodic, the existence of periodic solution are also obtained. Finally, by linearization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution.

Wan-Tong Li | Hai-Feng Huo

[1] P. H. Leslie. SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS , 1948 .

[2] Yoshiaki Muroya. Persistence and global stability for discrete models of nonautonomous Lotka–Volterra type , 2002 .

[3] P. H. Leslie. A STOCHASTIC MODEL FOR STUDYING THE PROPERTIES OF CERTAIN BIOLOGICAL SYSTEMS BY NUMERICAL METHODS , 1958 .

[4] Ravi P. Agarwal,et al. Advanced topics in difference equations , 1992 .

[5] J. Hofbauer,et al. Coexistence for systems governed by difference equations of Lotka-Volterra type , 1987, Journal of mathematical biology.

[6] Abdul-Aziz Yakubu,et al. Mutual exclusion versus coexistence for discrete competitive systems , 1991 .

[7] Abdul-Aziz Yakubu,et al. Geometry of exclusion principles in discrete systems , 1992 .

[8] Andrei Korobeinikov,et al. A Lyapunov function for Leslie-Gower predator-prey models , 2001, Appl. Math. Lett..

[9] Abdul-Aziz Yakubu,et al. Species extinction using geometry of level surfaces , 1993 .

[10] Wanbiao Ma,et al. A Necessary and Sufficient Condition for Permanence of a Lotka–Volterra Discrete System with Delays , 2001 .

[11] Wang Wendi,et al. Global stability of discrete models of Lotka-Volterra type , 1999 .

[12] Zhan Zhou,et al. Stable periodic solution of a discrete periodic Lotka–Volterra competition system , 2003 .