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Smale, S.; Williams, R. F.

The qualitative analysis of a difference equation of population growth. (English) Zbl 0342.92014

J. Math. Biol. 3, 1-4 (1976).
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Cited in 26 Documents

MSC:

92D25 Population dynamics (general)
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\textit{S. Smale} and \textit{R. F. Williams}, J. Math. Biol. 3, 1--4 (1976; Zbl 0342.92014)
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References:

[1] Beddington, S., Free, C., Lawton, S.: Dynamic complexity in predator prey models framed in differential equations. Nature 255, 58-60 (1975). · doi:10.1038/255058a0
[2] Block, L.: An example where topological entropy is continuous. (To appear.) · Zbl 0379.58016
[3] Bowen, R., Lanford, O.: Zeta functions of restrictions of the shift transformation. Global Analysis (Proc. Symp. Pure Math., Vol. XIV). Amer. Math. Soc. 1970, 43-49. · Zbl 0211.56501
[4] Fatou, P.: Sur les ?quations fonctionnelles, II. Bull. Soc. Math. France 48, 33-94 (1920).
[5] Guckenheimer, J.: Endomorphisms of the Riemann sphere, global analysis (Proc. Symp. Pure Math., Vol. XIV). Amer. Math. Soc. 1970, 95-123.
[6] Guckenheimer, J., Oster, G., Ipakchi, A.: The dynamics of density dependent population models. (To appear.)
[7] Hoppensteadt, F., Hyman, J.: Periodic solutions of a logistic difference equation. SIAM regional conference, University of Iowa, 1975, preprint.
[8] Jakobson, M.: Structure of polynomial mappings on a singular set. Math. USSR, Sbornik 6, 97-114 (1968). · Zbl 0208.34002 · doi:10.1070/SM1968v006n01ABEH001054
[9] Li, T. Y., Yorke, J.: Period three implies chaos. SIAM. J. Applied Math. (To appear.) · Zbl 0351.92021
[10] May, R., Oster, G.: Bifurcations and dynamic complexity in simple ecological models, preprint.
[11] Nitecki, Z., Non-singular endomorphisms of the circle, Global Analysis (Proc. Symp. Pure Math., Vol. XIV). Amer. Math. Soc. 1970, 203-220.
[12] Peixoto, M.: Dynamical Systems (editor). New York: Academic Press 1973. · Zbl 0265.00011
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