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Nunney, Len

The influence of the type 3(sigmoid) functional response upon the stability of predator-prey difference models. (English) Zbl 0447.92019

Theor. Popul. Biol. 18, 257-278 (1980).
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Cited in 6 Documents

MSC:

92D25 Population dynamics (general)

Keywords:

sigmoid functional responses; discrete-generation predator-prey model; difference equation models; stability; self-regulation
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References:

[1] Beddington, J. R., Mutual interference between parasites or predators and its effect on searching efficiency, J. Anim. Ecol, 44, 331-340 (1975)
[2] Beddington, J. R.; Free, C. A.; Lawton, J. H., Dynamic complexity in predator-prey models framed in difference equations, Nature (London), 255, 58-60 (1975)
[3] Beddington, J. R.; Free, C. A.; Lawton, J. H., Concepts of stability and resilience in predator-prey models, J. Anim. Ecol, 45, 791-816 (1976)
[4] Beddington, J. R.; Free, C. A.; Lawton, J. H., Characteristics of successful natural enemies in models of biological control of insect pests, Nature (London), 273, 513-519 (1978)
[5] Cook, L. M., Oscillations in the simple logistic growth model, Nature (London) (1965)
[6] DeAngelis, D. L., Estimates of predator-prey limit cycles, Bull. Math. Biol, 37, 291-300 (1975) · Zbl 0309.92004
[7] Hassell, M. P., The Dynamics of Arthropod Predator-Prey Systems (1978), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 0429.92018
[8] Hassell, M. P.; Comins, H. N., Sigmoid functional responses and population stability, Theor. Pop. Biol, 14, 62-67 (1978) · Zbl 0386.92010
[9] Hassell, M. P.; Lawton, J. H.; Beddington, J. R., Sigmoid functional responses by invertebrate predators and parasitoids, J. Anim. Ecol, 46, 249-262 (1977)
[10] Hassell, M. P.; May, R. M., Stability in insect host-parasite models, J. Anim. Ecol, 42, 693-736 (1974)
[11] Holling, C. S., The components of predation as revealed by a study of small-mammal predation of the European pine sawfly, Canad. Entomol, 91, 293-320 (1959)
[12] Holling, C. S., Some characteristics of simple types of predation and parasitism, Canad. Entomol, 91, 395-398 (1959)
[13] May, R. M., Biological populations with non-overlapping generations: stable points, stable cycles and chaos, Science, 186, 645-647 (1974)
[14] May, R. M.; Oster, G. F., Bifurcations and dynamic complexity in simple ecological models, Amer. Natur, 110, 573-599 (1976)
[15] Murdoch, W. W.; Oaten, A., Predation and population stability, Advan. Ecol. Res, 9, 1-125 (1975)
[16] Nicholson, A. J.; Bailey, V. A., The balance of animal populations, Part 1, (Proc. Zool. Soc. London, 3 (1935)), 551-598
[17] Nunney, L., The stability of complex model ecosystems, Amer. Natur, 115, 161-176 (1980)
[18] Oaten, A.; Murdoch, W. W., Functional response and stability in predator-prey systems, Amer. Natur, 109, 299-318 (1975)
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