Global bifurcation and long time behavior of the Volterra-Lotka ecological model

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 1, 2001, Pages 133-142

  Li, Kaitai ^a   Wang, Lizhou ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034747506     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401002067     Document Type: Article

References (23)

1. Blat, J. & Brown, K. J. [1985] "Global bifurcation of positive solutions in some systems of elliptic equations, SIAM. J. Math. Anal. 17, 1339-1353.
2. Cohen, D. S. & Laetsch, T. W. [1970] "Nonlinear boundary value problems suggested by chemical reactor theory," J. Diff. Eqs. 7, 217-226.
3. Cosner, C. & Lazer, A. C. [1984] "Stable coexistence state in the Volterra-Lotka competition model with diffusion," SIAM J. Math. Anal. 44, 1112-1132.
4. Dancer, E. N. [1984] "On positive solutions of some pairs of differential equations," Trans. Amer. Math. Soc. 284, 729-743.
5. Dancer, E. N. [1985] "On positive solutions of some pairs of differential equations II," J. Diff. Eqs. 60, 236-258.
6. Dancer, E. N. [1991] "On the existence and uniqueness of positive solutions for competing species models with diffusion," Trans. Amer. Math. Soc. 326, 829-859.
7. Dancer, E. N. & Du, Y. [1995a] "Positive solutions for a three-species competition system with diffusion-I. General existence result," Nonlin. Anal. Th. Meth. Appl. 24, 337-357.
8. Dancer, E. N. & Du, Y. [1995b] "Positive solutions for a three-species competition system with diffusion-II. The case of equal birth rates," Nonlin. Anal. Th. Meth. Appl. 24, 359-373.
9. Decker, D. W. & Keller, H. B. [1980] "Multiple limit point bifurcation," J. Math. Anal. Appl. 75, 417-430.
10. Deimling, K. [1985] Nonlinear Functional Analysis, (Springer-Verlag, NY, Heidelberg, Berlin, Tokyo).
11. Feng, W. [1993] "Coexistence, stability, and limiting behavior in a one-predator-two-prey model," J. Math. Anal. Appl. 179, 592-609.
12. Korman, P. & Leung, A. [1987] "On the existence and uniqueness in the Volterra-Lotka ecological models with diffusion," Appl. Anal. 26, 145-160.
13. Lakos, N. [1990] "Existence of steady-states solutions for a one-predator-two-prey system," SIAM J. Math. Anal. 21, 647-659.
14. Leung, A. [1982] "Monotone schemes for semilinear elliptic systems related to ecology," Math. Meth. Appl. Sci. 4, 272-285.
15. Leung, A. [1984] "A study of three species prey-predator reaction-diffusion by monotone schemes," J. Math. Anal. Appl. 100, 583-604.
16. Lu, X. & Feng, W. [1994] "Dynamics and numerical simulations of food-chain populations," Appl. Math. Comp. 65, 335-344.
17. Mckenna, P. J. & Walter, W. [1984] "On the Dirichlet problem for elliptic systems," Appl. Anal. 21, 207-224.
18. Pao, C. V. [1981] "Coexistence and stability of a competition-diffusion system in population dynamics," J. Math. Anal. Appl. 83, 54-76.
19. Pao, C. V. [1982] "On nonlinear reaction-diffusion systems," J. Math. Anal. Appl. 87, 165-198.
20. Pao, C. V. [1997] "Dynamics of reaction-diffusion systems and applications," Nonlin. Anal. Th. Meth. Appl. 30, 3371-3377.
21. Temam, R. [1988] Infinite Dimensional Dynamical Systems in Mechanics and Physics, (Springer-Verlag, NY).
22. Zhen, M. [1991] "Bifurcations of a simplified buckling problem and the effect of discretizations," Manuscripta Math. 71, 225-252.
23. Zhou, L. & Pao, C. V. [1982] "Asymptotic behavior of a competition-diffusion system in population dynamics," Nonlin. Anal. Th. Meth. Appl. 6, 1163-1184.