On the Dynamics of Predator-Prey Models with the Beddington-DeAngelis Functional Response

Journal of Mathematical Analysis and Applications

Volumn 257, Issue 1, 2001, Pages 206-222

  Cantrell, Robert Stephen ^a   Cosner, Chris ^a  

^a UNIVERSITY OF MIAMI   (United States)

Author keywords

Predator prey; reaction diffusion; functional response; permanence; uniform persistence

Indexed keywords

EID: 0038750243     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7343     Document Type: Article

References (21)

1. Avila E., Cantrell R. S. Permanence of three competitors in seasonal ecological models with spatial heterogeneity. Can. Appl. Math. Quart. 5:1997;145-169.
2. Beddington J. R. Mutual interference between parasites or predators and its effect on searching efficiency. J. Animal Ecol. 44:1975;331-340.
3. Cantrell R. S., Cosner C. Diffusive logistic equations with indefinite weights: population models in disrupted environments. Proc. Roy. Soc. Edinburgh Sect. A. 112:1989;293-318.
4. Cantrell R. S., Cosner C. Diffusive logistic equations with indefinite weights: population models in disrupted environments II. SIAM J. Math. Anal. 22:1991;1043-1064.
5. Cantrell R. S., Cosner C. Practical persistence in ecological models via comparison methods. Proc. Roy. Soc. Edinburgh Sect. A. 126:1996;247-272.
6. Cantrell R. S., Cosner C. Practical persistence in diffusive food chain models. Nat. Res. Modeling. 11:1998;21-34.
7. Cantrell R. S., Cosner C. Bounds on trajectories in diffusive predator-prey models. Advances in Mathematical Population Dynamics: Molecules, Cells, and Man (Proceedings of the 4th International Conference in Mathematical Population Dynamics). 1997;World Scientific, Singapore. p. 733-746.
8. Cantrell R. S., Cosner C., Hutson V. Permanence in ecological systems with spatial heterogeneity. Proc. Roy. Soc. Edinburgh Sect. A. 123:1993;533-559.
9. Cantrell R. S., Cosner C., Hutson V. Permanence in some diffusive Lotka-Volterra models for three interacting species. Dynam. Systems Appl. 2:1993;505-530.
10. Cosner C. Pointwise a priori bounds for strongly coupled semi-linear systems of parabolic partial differential equations. Indiana U. Math. J. 30:1981;607-620.
11. Cosner C., DeAngelis D. L., Ault J. S., Olson D. B. Effects of spatial grouping on the functional response of predators. Theoret. Population Biol. 56:1999;65-75.
12. DeAngelis D. L., Goldstein R. A., O'Neill R. V. A model for trophic interaction. Ecology. 56:1975;881-892.
13. Goh B. S. Global stability in two-species interactions. J. Math. Biol. 3:1976;313-318.
14. Hale J. K., Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20:1989;388-395.
15. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. 1981;Springer-Verlag, Berlin.
16. Hess P. Periodic-Parabolic Boundary Value Problems and Positivity. Pitman Lecture Notes Mathematics. 247:1991;Longman Technical and Scientific, Harlow.
17. Hutson V., Schmitt K. Permanence in dynamical systems. Math. Biosci. 111:1992;1-71.
18. Kuang Y., Baretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 36:1998;389-406.
19. Morgan J. Boundedness and decay results for reaction-diffusion systems. SIAM J. Math. Anal. 21:1990;1172-1189.
20. Ruxton G., Gurney W. S. C., DeRoos A. Interference and generation cycles. Theoret. Population Biol. 42:1992;235-253.
21. Senn S. On a nonlinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics. Comm. Partial Differential Equations. 8:1983;1199-1228.