A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays

Journal of Mathematical Analysis and Applications

Volumn 256, Issue 1, 2001, Pages 162-174

  Saito, Yasuhisa ^a   Ma, Wanbiao ^a   Hara, Tadayuki ^a  

^a Osaka Prefecture University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035315099     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7303     Document Type: Article

References (10)

1. Freedman H. I., Ruan S. Uniform persistence in functional differential equations. J. Differential Equations. 115:1995;173-192.
2. Hofbauer J., Hutson V., Jansen W. Coexistence for systems governed by difference equations of Lotka-Volterra type. J. Math. Biol. 25:1987;553-570.
3. Hofbauer J., Sigmund K. Dynamical Systems and the Theory of Evolution. 1988;Cambridge Univ. Press, Cambridge.
4. Hutson V., Moran W. Persistence of species obeying difference equations. J. Math. Biol. 15:1982;203-213.
5. Kuang Y. Delay Differential Equations with Applications in Population Dynamics. 1993;Academic Press, New York.
6. Lu Z., Takeuchi Y. Permanence and global attractivity for competitive Lotka-Volterra systems with delay. Nonlinear Anal. 22:1994;847-856.
7. Lu Z., Wang W. Permanence and global attractivity for Lotka-Volterra difference systems. J. Math. Biol. 39:1999;269-282.
8. Takeuchi Y. Global Dynamical Properties of Lotka-Volterra Systems. 1996;World Scientific, Singapore.
9. Wang W., Ma Z. Harmless delays for uniform persistence. J. Math. Anal. Appl. 158:1991;256-268.
10. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. 1990;Springer-Verlag, New York.