×

zbMATH — the first resource for mathematics

How do ecosystems respond to external perturbations? (English) Zbl 0985.37105
In this paper the influence of environmental perturbations on evolutionary modes of model ecosystems is studied. The authors show that the method discussed in the paper is relevant to study the ecosystem response to both types of perturbations – seasonal and sudden. Both basin boundary structures and three distinct model systems representing three sets of different ecological situations are discussed.

MSC:
37N25 Dynamical systems in biology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Software:
Dynamics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DeAngelis DL. Dynamics of nutrient cycling and food webs. London: Chapman & Hall, 1992
[2] Neubert, M.G.; Caswell, H., Ecology, 78, 3, 653, (1997)
[3] Schmitz OJ. Ecology 1997;78(1):55 and references therein
[4] DeAngelis, D.L.; Bartell, S.M.; Brenkert, A.L., Amer naturalist, 134, 778, (1989)
[5] Harrison, G.W., Amer naturalist, 113, 659, (1979)
[6] O’Neill, R.V., Ecology, 57, 1244, (1976)
[7] Harwell, M.A.; Cropper, W.P.; Ragsdale, H.L., Ecology, 58, 660, (1977)
[8] DeAngelis, D.L., Ecology, 61, 764, (1980)
[9] Ives, A.R., Ecolog monogr, 65, 217, (1995)
[10] Lepš, J.J.; Osbornová, K.; Rejmanek, M., Vegetatio, 50, 53, (1982)
[11] Pimm, S.L.; Lawton, J.H., Nature, 268, 329, (1977)
[12] Cottingham, K.L.; Carpenter, S.R., Ecology, 75, 2127, (1994)
[13] Pimm, S.L., Theor population biol, 16, 144, (1979)
[14] Armstrong, R.A., Amer naturalist, 120, 391, (1982)
[15] Tilman, G.D., Ecology, 65, 1445, (1984)
[16] Krebs CJ. Ecological methodology. New York: Harper & Row, 1989
[17] Pimm SL. The balance of nature? Chicago: University of Chicago press, 1991
[18] Ritchie, M.E.; Tilman, G.D., Oecologia, 89, 524, (1992)
[19] Schaffer, W.M., Ecology, 66, 93, (1985) · Zbl 0609.92034
[20] Schaffer, W.M.; Kot, M., Bioscience, 35, 342, (1985)
[21] Ruelle D. Chaotic evolution and strange attractors. Cambridge: Cambridge University Press, 1989 · Zbl 0683.58001
[22] Ott E. Chaos in dynamical systems. Cambridge: Cambridge University Press, 1993 · Zbl 0792.58014
[23] McDonald, S.W.; Grebogi, C.; Ott, E.; Yorke, J.A., Physica, 17D, 125, (1985)
[24] Grebogi, C.; Ott, E.; Yorke, J.A., Phys rev lett, 50, 935, (1983)
[25] Allee WC, Emerson AE, Park O, Schmidt T. Principles of animal ecology. London: Saunders, 1949
[26] Lande, R., Science, 241, 1455, (1988)
[27] Hsu, S.; Huang, T., SIAM J applied math, 55, 3, 763, (1995)
[28] Upadhyay, R.K.; Rai, V., Chaos, solitons & fractals, 8, 12, 1933, (1997)
[29] Upadhyay, R.K.; Iyengar, S.R.K.; Rai, V., Int J bifurc chaos, 8, 6, 1325, (1998) · Zbl 0935.92037
[30] May RM. Stability and complexity in model ecosystems. Princeton, NJ: Princeton University Press, 1973
[31] Rai, V.; Kumar, V.; Pande, L.K., IEEE trans systems, Man and cybernetics, 21, 1, 261, (1991)
[32] Jørgensen SE, editor. Handbook of environmental data and ecological parameters. New York: Pergamon, 1979:142
[33] Nusse HE, Yorke JA. Dynamics: numerical explorations. Berlin: Springer, 1994
[34] Peliti L, Vulpiani A, editors. Measures of complexity. Berlin: Springer, 1988 · Zbl 0707.68003
[35] Poon, L.; Grebogi, C., Phys rev lett, 75, 22, 4023, (1995)
[36] Garrido MS, Mendes VR, editors. Complexity in physics and technology. Singapore: World Scientific, 1993
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.