Global asymptotic behavior of a two-dimensional difference equation modelling competition

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 7, 2003, Pages 1765-1776

  Clark, Dean ^a   Kulenovic M R S ^a   Selgrade, James F ^b  

^a University of Rhode Island   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Asymptotic behavior; Monotonicity; Stability; Stable manifold

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; INITIAL VALUE PROBLEMS; THEOREM PROVING;

ASYMPTOTIC BEHAVIOR;

DIFFERENCE EQUATIONS;

EID: 0037333658     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00294-8     Document Type: Article

References (12)

1. Clark D., Kulenović M.R.S. On a coupled system of rational difference equations. Comput. Math. Appl. 43:2002;849-867.
2. Dancer E.N., Hess P. Stability of fixed points for order-preserving discrete-time dynamical systems. J. Reine. Angew. Math. 419:1991;125-139.
3. Franke J.E., Yakubu A.-A. Mutual exclusion verses coexistence for discrete competitive systems. J. Math. Biol. 30:1991;161-168.
4. Franke J.E., Yakubu A.-A. Geometry of exclusion principles in discrete systems. J. Math. Anal. Appl. 168:1992;385-400.
5. Hale J., Kocak H. Dynamics and Bifurcations. 1991;Springer, New York.
6. Hassell M.P., Comins H.N. Discrete time models for two-species competition. Theoret. Population Biol. 9:1976;202-221.
7. Hess P. Periodic-parabolic Boundary Value Problems and Positivity. Pitman Research Notes in Mathematics Series. Vol. 247:1991;Longman Scientific & Technical, Essex, UK.
8. Hess P., Lazer A.C. On an abstract competition model and applications. Nonlinear Anal. TMA. 16:1991;917-940.
9. Lakshmikantham V., Triggiante D. Theory of Difference Equations. 1988;Academic Press, Boston.
10. Robinson C. Stability, Symbolic Dynamics, and Chaos. 1995;CRC Press, Boca Raton, FL.
11. Selgrade J.F., Ziehe M. Convergence to equilibrium in a genetic model with differential viability between the sexes. J. Math. Biol. 25:1987;477-490.
12. Smith H.L. Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. 1995;American Mathematical Society, Providence, RI.