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Catastrophe theory as applied to the social and biological sciences: A critique. (English) Zbl 0389.92002


MSC:

92-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology
58K35 Catastrophe theory
92B05 General biology and biomathematics
91D99 Mathematical sociology (including anthropology)
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[1] Abraham, R., (1972a) ?Introduction to Morphology?, Quatrieme Re \(\mathop c\limits^` \) ontre entre Math. et Phys.. 4, Fasc. 1, Dept. Math. de l’Universite de Lyon, Tome 9, pp. 38-114.
[2] Andreski, S., (1972a)Social Sciences as Sorcery, St. Martin’s Press.
[3] Bronowski, J., (1973a)The Ascent of Man, Little Brown and Co.
[4] Cole, E. S., (1968a)Membranes, Ions and Impulses, University of California Press.
[5] Ehrenstein, G. and Lecar, H., (1972) ?The Mechanism of Signal Transmission in Nerve Axons?,Ann. Rev. Biophys. Bioeng. 1, 347-368. · doi:10.1146/annurev.bb.01.060172.002023
[6] FitzHugh, R., (1969a) ?Mathematical Models of Excitation and Propagation in Nerve?, in H. P. Swan (ed.),Biological Engineering, McGraw-Hill. · Zbl 0181.55002
[7] Golubitsky, M., and Guillemin, V., (1974a) ?Stable Mappings and Their Singularities?,Graduate Texts in Mathematics 14, Springer-Verlag, Inc. · Zbl 0294.58004
[8] Hodgkin, A. L. and Huxley, A. F., (1952a) ?A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve?,J. Physiol. 117, 500-544.
[9] Hodgkin, A. L., (1964a)The Conduction of Nervous Impulse, Liverpool University Press.
[10] Hodgkin, A. L., Huxley, A. F., and Katz, M., (1952) ?Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of Loligo?,J. Physiol. 116, 424-448.
[11] Isnard, C. A., and Zeeman, E. C., (1974a) ?Some Models from Catastrophe Theory in the Social Sciences? in L. Collins (ed.),Use of Models in the Social Sciences, Tavistock, London, 1974.
[12] Jones, D. D., (1975a) ?The Application of Catastrophe Theory to Ecological Systems?,International Institute for Applied Systems Analysis, (IIASA) Research Report, Schoss Laxenburg, 2361 Laxenburg, Austria, June 1975.
[13] Kline, M., (1964a)Mathematics in Western Culture, Oxford University Press paperbacks, 1974. · Zbl 0154.24102
[14] Lorenz, K., (1967a)On Aggression, Bantam Books.
[15] Sussman, H. J., (1975a) ?Catastrophe Theory?,Synthese,31, 229-270. · Zbl 0309.58008 · doi:10.1007/BF00485979
[16] Sussmann, H. J., (1976a) ?Catastrophe Theory, a Preliminary Critical Study?,Proceedings of the 1976 Biennial Meeting of the Philosophy of Science Association, Chicago, Oct. 1976.
[17] Thom, R., (1974a), ?La Théorie des Catastrophes: état présent et perspectives?, in A. Manning (ed.),Dynamical Systems ? Warwick 1974, Springer Verlag Lecture Notes in Mathematics 468, 366-372.
[18] Thom, R., (1974b) ?Answer to Christopher Zeeman’s Reply?,ibid, 384-389.
[19] Thom, R., (1975a)Structural Stability and Morphogenesis, W. A. Benjamin, Inc. · Zbl 0303.92002
[20] Thom, R., (1975b) ?D’un modèle de la science à une science des modèles?,Synthese 31, 359-374. · Zbl 0309.00044 · doi:10.1007/BF00485984
[21] Zeeman, E. C., (1971a) ?Geometry of Catastrophe?,Times Literary Supplement, Dec. 10, 1971.
[22] Zeeman, E. C., (1972a) ?Differential Equations for the Heartbeat and the Nerve Impulse?, C. H. Waddington (ed.),Towards a Theoretical Biology, Vol. 4, Edinburgh University Press, pp. 8-67.
[23] Zeeman, E. C., (1973a) ?Applications of Catastrophe Theory?,Int. Conf. on Manifolds, Tokyo University, 1973. · Zbl 0311.58004
[24] Zeeman, E. C., (1974a) ?Levels of Structure in Catastrophe Theory?,Proceedings of the International Congress of Mathematics, Vol.2, pp. 533-546.
[25] Zeeman, E. C., (1974b) ?On the Unstable Behavior of Stock Exchanges?,J. Math. Economics 1, 39-49. · Zbl 0297.90002 · doi:10.1016/0304-4068(74)90034-2
[26] Zeeman, E. C., (1974c) ?Primary and Secondary Waves in Developmental Biology. Some Mathematical Questions in Biology, VIII?, Lectures on Mathematics in the Life Sciences,Amer. Math. Society, Providence, 1974, pp. 69-163. · Zbl 0317.92002
[27] Zeeman, E. C., (1976a) ?Catastrophe Theory?,Scientific American, April 1976, pp. 65-83.
[28] Zeeman, E. C., Hall, C. S., Harrison, P. J., Marriage, G. H., and Shapland, P. H., (1976b) ?A Model for Institutional Disturbances?,J. Math. Stat. Psychology,29, 73. · Zbl 0339.92014
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