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Casten, Richard G.; Case, Ted J.

The effect of dispersal on the stability of some model ecological communities. (English) Zbl 0397.92027

Math. Biosci. 43, 281-288 (1979).
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MSC:

92D40 Ecology

Keywords:

Equilibrium Point; Ecological Communities; Dispersal; Consumer; Resource; Local Stability; Diffuson Terms
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References:

[1] Allen, J. C., Mathematical models of species interactions in time and space, Amer. Nat., 109, 319-342 (1975)
[2] Bellman, R., Introduction to Matrix Analysis (1970), McGraw-Hill: McGraw-Hill New York · Zbl 0216.06101
[3] T.J. Case and R.G. Casten, Global stability and multiple domains of attraction in ecological system, Amer. Nat.; T.J. Case and R.G. Casten, Global stability and multiple domains of attraction in ecological system, Amer. Nat.
[4] Casten, R. G.; Holland, C. S., Stability properties of solutions to systems of reaction-diffusion equations, SIAM J. Appl. Math., 33, 353-360 (1977) · Zbl 0372.35044
[5] Goh, B. S., Global stability in many species systems, Amer. Nat., 111, 135-143 (1977)
[6] Hassell, M. D.; May, R. M., Aggregation of predators and insect parasites and its effect on stability, J. Anim. Ecol., 43, 567-594 (1974)
[7] Hastings, A., Spatial heterogeneity and the stability of predator-prey systems, Theoret. Population Biology, 12, 37-48 (1977) · Zbl 0371.92016
[8] Hilborn, R., The effect of spatial heterogeneity on the persistence of predator-prey interactions, Theoret. Population Biology, 8, 346-355 (1975)
[9] Horn, H. S.; MacArthur, R. H., Competition among fugitive species in a harlequin environment, Ecology, 53, 749-752 (1972)
[10] Levandowsky, M.; White, B. S., Randomness, time scales and the evolution of biological communities, Evol. Biology, 10, 69-161 (1977)
[11] Levin, S., Dispersion and population interactions, Amer. Nat., 108, 207-228 (1974)
[12] Levins, R., Evolution in communities near equilibrium, (Cody, M. L.; Diamond, J. M., Ecology and Evolution of Communities (1975), Belknap Press: Belknap Press Cambridge), 16-50
[13] Levins, R.; Culver, D., Regional coexistence of species and competition between rare species, Proc. Nat. Acad. Sci. U.S.A., 68, 1246-1248 (1971) · Zbl 0217.57702
[14] MacArthur, R. H., Geographical Ecology (1972), Harper and Row: Harper and Row New York
[15] Smith, J. Maynard, Models in Ecology (1974), Cambridge U.P: Cambridge U.P Cambridge · Zbl 0312.92001
[16] Okubo, A., Diffusion induced instability in model ecosystems: another possible explanation of patchiness, (Tech Rept. 86 (1974), Chesapeake Bay Inst., John Hopkins Univ)
[17] Othmer, H. G.; Scriven, L. E., Interactions of reaction and diffusion in open systems, Ind. Eng. Chem. Fund., 8, 302-313 (1969)
[18] Roughgarden, J., Resource partitioning among competing species: a coevolutionary approach, Theoret. Population Biology, 9, 388-425 (1976) · Zbl 0355.92015
[19] Segel, L. A.; Jackson, J. L., Dissipative structure: an explanation and an ecological example, J. Theoret. Biol., 137, 545-559 (1972)
[20] Slatkin, M., Competition and regional coexistence, Ecology, 55, 128-134 (1974)
[21] Turing, A. M., On the chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London Ser. B., 237, 27-72 (1952) · Zbl 1403.92034
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