Survival and extinction in competitive systems

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 2, 2008, Pages 708-717

  Ahmad, Shair ^a   Stamova, Ivanka ^b  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

^b BURGAS FREE UNIVERSITY   (Bulgaria)

Author keywords

(I, J) condition; Extinction; Growth rate; Interaction coefficients; Permanence; Persistence

Indexed keywords

BIODIVERSITY; ENVIRONMENTAL IMPACT; LINEAR MATRIX INEQUALITIES; TWO DIMENSIONAL;

EXTINCTION; INTERACTION COEFFICIENTS; PERMANENCE; PERSISTENCE; TWO-DIMENSIONAL LOTKA-VOLTERRA SYSTEMS;

NONLINEAR SYSTEMS;

EID: 37249042675     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.12.011     Document Type: Article

References (15)

1. Ahmad S., and Lazer A.C. Necessary and sufficient average growth in a Lotka-Volterra system. Nonlinear Anal. 34 (1998)
2. Ahmad S., and Lazer A.C. Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system. Nonlinear Anal. 40 (2000)
3. Ahmad S., and Lazer A.C. Average growth and extinction in a competitive Lotka-Volterra system. Nonlinear Anal. 62 (2005)
4. Ahmad S., and Lazer A.C. Average growth and total permanence in a competitive Lotka-Volterra system. Ann. Mat. 185 (2006)
5. Ahmad S., and Stamova I.M. Almost necessary and sufficient conditions for survival of species. Nonlinear Anal. Real World Appl. 5 (2004)
6. Ahmad S., and Stamova I.M. Partial persistence and extinction in N-dimensional competitive systems. Nonlinear Anal. 60 (2005)
7. Bellman R. Matrix Analysis. second ed. (1975), McGraw-Hill, New York
8. Hallam T., Svoboda L., and Gard T. Persistence and extinction in three species Lotka-Volterra competitive systems. Math. Biosci. 46 (1979)
9. Hartman P. Ordinary Differential Equations (1973), P. Hartman, Baltimore
10. Hofbauer J., and Sigmund K. The Theory of Evolution and Dynamical Systems (1988), Cambridge University Press, New York
11. Jansen W. A permanence theorem for replicator and Lotka-Volterra systems. J. Math. Biol. 25 (1986)
12. May R.M., and Leonard W. Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29 (1975)
13. Redheffer R. Lotka-Volterra systems with constant interaction coefficients. Nonlinear Anal. 46 (2001)
14. Takeuchi Y. Global Dynamical Properties of Lotka-Volterra Systems (1996), World Scientific, Singapore
15. Waltman P. A brief survey of persistence in dynamical systems. In: Busenberg, and Martelli M. (Eds). Delay Differential Equations and Dynamical Systems. fifth ed. (1991), Springer, Berlin