Abstract
Suppose we have a family of “potential” functions φλ:IRn→ IR, evolving with λ (=time/varying load on a system/temperature/magnetic field/…) and that for any fixed φ the state x = (x,…, xn)ɛIRntends to “occupy” a minimum of φ (More exactly, for most such systems, the difference of x and some x0at which φ has a minimum dies away exponentially.) The set of minima of φλvaries with λ in ways discussed in elastic stability theory [TH], thermodynamies [C],economics [B], laser dynamics [Ha],etc. - choosing a merely representative reference in each case - and most generally in catastrophe theory [Th,Z,PS]. How does x vary in consequence?
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Y. Balasko: The behaviour of economic equilibria: a Catastrophe Theory Approach, Behavioral Science 23, 1978, 375–382
E. Benoit, J.-L. Callot, F. Diener, M. Diener: Chasse au Canard, Publ. de l’Institut de Recherche Mathématique Avancée, Strasbourg, 1980
H.B. Callen: Thermodynamics, Wiley, N.Y. and London, 1960
M. Diener: Etude Génerique des Canards, Thèse de doctorat, Strasbourg, 1981
DD] F. Diener, M. Diener: Quelques Formulas Relatives aux Canards, to appear
H. Haken: Synergetics, An Introduction, 2nd ed., Springer Series in Synergetics, Vol. 1 ( Springer Berlin, Heidelberg, New York 1978 )
H. Hrbacek; Non-standard Set Theory, Am.Math.Month!y (86), 1 979 pp. 659–677
L.D. Landau, E.M. Lifshitz; Statistical Physics (trans.Peierls and Peierls), 2nd English edition, Pergamon, Oxford and New York, 1959
R. Lutz, M. Gose; Non-Standard Analysis, a Practical Guide, ‘Lecture Notes in Mathematics’ (Springer Berlin, Heidelberg, New York 1981 )
E. Nelson; Internal Set Theory, B.A.M.S. (83) no. 6, 1977, pp 1165–1198
T. Poston, I.N. Stewart; Catastrophe Theory and its Applications, Pitman, London 1978
T. Poston: “Various Catastrophe Machines”, in Structure Stability, The Theory of Catastrophes, and Applications in the Sciences, ed. by P. Hilton; Lecture Notes in Mathematics, Vol. 525 ( Springer Berlin, Heidelberg, New York 1976 ) pp. 111–126
A. Robinson; Non Standard Analysis, 2nd. edition, Elsevier, New York, 1974
O.O.E. Rössler: “Continuous Chaos”, in Synergetics, A Workshop, ed. by H. Haken, Springer Series in Synergetics, Vol. 2 ( Springer Berlin, Heidelberg, New York 1977 ) pp. 184–197
F. Takens: “Constrained Equations: A Study of Implicit Differential Equations and Their Discontinuous Solutions”, in Structural Stability, the Theory of Catastrophes, and Their Applications in the Sciences, ed. by P.J. Hilton, Lecture Notes in Mathematics, Vol. 525 ( Springer Berlin, Heidelberg, New York 1976 ) pp. 143–234
F. Takens: Implicit Differential Equations: Some Open Problems, in Singularités d’Applications Différentiables, ed. by O. Burlet, F. Ronga, Lecture Notes in Mathematics, Vol. 535 ( Springer Berlin, Heidelberg, New York 1976 ) pp. 237–253
R. Thom, Stabilité Structurelle et Morphogenese, Benjamin, New York 1972, translated D.H. Fowler as Structural Stability and Morphogenesis, Benjamin, Addison-Wesley, New York, 1975
J.M.T. Thompson, G.W. Hunt: A General Theory of Elastic Stability, Wiley, London, New York, 1973
U. Weiß: The Uses of Path Integrals for Diffusion Processes, these proceedings
E.C. Zeeman: Catastrophe Theory: Selected Papers 1972–1977, Addison-Wesley, Reading, Mass. 1977
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Diener, M., Poston, T. (1981). On the Perfect Delay Convention or the Revolt of the Slaved Variables. In: Haken, H. (eds) Chaos and Order in Nature. Springer Series in Synergetics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68304-6_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-68304-6_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-68306-0
Online ISBN: 978-3-642-68304-6
eBook Packages: Springer Book Archive