Chaos and Order in Nature

Proceedings of the International Symposium on Synergetics at Schloss Elmau, Bavaria, April 27 – May 2, 1981

Springer Series in Synergetics, Vol. 11

1984 (corr. Print.), Springer-Verlag, ISBN 3-540-11101-8




Prof. Dr. Dr. h.c. Hermann Haken

Institut fŸr Theoretische Physik

UniversitŠt Stuttgart

Pfaffenwaldring 57/IV

D-7000 Stuttgart 80, Fed. Rep. of Germany






Part I: Introduction


H. Haken: Chaos and order in nature



Part II: Fluid dynamics. Order and chaos in fluid dynamics


P. BergŽ (Service de Physique du Solide RŽsonance MagnŽtique, C.E.N.-Saclay, F-91191 Gif sur Yvette): Rayleigh-Benard convection in high Prandtl number fluid


S. Fauve, A. Libchaber (Ecole Normale SupŽrieure, Groupe du Physique des Solides, F-Paris): Rayleigh-Benard experiment in a low Prandtl number fluid, mercury


F.H. Busse (Max-Planck-Institut fŸr Physik und Astrophysik, D-8046 Garching): Transition to turbulence via the statistical limit cycle route


A. BrandstŠter, G. Pfister, I. Rehberg, E.O. Schulz-DuBois (Institut fŸr Angewandte Physik der UniversitŠt Kiel, D-2300 Kiel): Divergence of coherence length and excitation of resonance in Taylor vortex flow


A. HŸbler, G. Schubert (Physik-Dept. E15 1 E13, Technische UniversitŠt MŸnchen, D-8046 Garching);  G. Meyer-Kress (Institut fŸr Theoretische Physik der UniversitŠt Stuttgart, D-7000 Stuttgart): Non-equilibrium phase transitions in a KundtÕs tube



Part III: Chaos in fluids, solid state physics, and chemical reactions


I.S. Aranson, M.I. Rabinovich, M.M. Sushchik (Institute of Applied Physics, Academy of Sciences of the USSR, Gorky): Stochastization of coherent structures by a periodic field


B.A. Huberman (Groupe de Physique des Solides de lÕEcole Normale SupŽrieure, UniversitŽ Paris VII, Paris): Turbulence and scaling in solid state physics


C. Vidal (Centre de Recherches Paul Pascal, F-33405 Talence): Dynamic instabilities observed in the Belousev-Zhabotinsky System



Part IV: Instabilities and bifurcations: theoretical approaches


G.R. Sell (School of Mathematics, University of Minnesota, Minneapolis, MN 55455): Hopf-Landau bifurcation near strange attractors


J.D. Gibbon (Dept. of Mathematics, Imperial College of Science and Technology, London SW7 2BZ): Dispersive instabilities in nonlinear systems: the real and complex Lorenz equation


D.F. Walls, P. Zoller (Institut fŸr Theoretische Physik, UniversitŠt Innsbruck, Innsbruck); P.D. Drummond (Dept. of Physics and Astronomy, University of Rochester, Rochester, NY 14627); C.V. Kunasz (Joint Institute for Laboratory Astrophysics, University of Colorado and National Bureau of Standards, Boulder, CO 80304): Bifurcations and multistability in nonlinear optics



Part V: plasma instabilities


H. Wilhelmsson (Institute for Electromagnetic Field Theory, Chalmers University of Technology, S-41296 Gšteborg): Coherent wave interactions in plasma and active molecular media


E. RŠuchle (Institut fŸr Plasmaforschung, UniversitŠt Stuttgart, D-7000 Stuttgart): Instability as a property of plasma states


H. Krompholz, G. Herziger (Institut fŸr Angewandte Physik, Technische Hochschule Darmstadt, D-6100 Darmstadt): Phenomena of self organization in dense plasma



Part VI: Phase transitions


Bai-lin Hao (FacultŽ des Sciences, UniversitŽ Libre de Bruxelles, B-1050 Bruxelles): Closed-form approximation and interpolation formulae for the 3-dimensional Ising model



Part VII: Path integrals: recent developments


H. Leschke (Institut fŸr Theoretische Physik, UniversitŠt DŸsseldorf, D-4000 DŸsseldorf): Path integral approach to fluctuations in dynamic processes


Ch. Wissel (Fachbereich Physik, UniversitŠt Marburg, D-3550 Marburg): Definitions of path integrals for general diffusion processes


U. Weiss (Institut fŸr Theoretische Physik, UniversitŠt Stuttgart, D-7000 Stuttgart): The uses of path integrals for diffusion in bistable potentials



Part VIII: General systems approaches


W. Ebeling (Sektion Physik PB 04, Humbolt-UniversitŠt Berlin, D-1086 Berlin): Structural stability of stochastic systems


W. Mende (Institute of Geography and Geoecology, Academy of Sciences of the GDR); M. Peschel (Scientific Dept. of Mathematics/ Cybernetics, Academy of Sciences of the GDR): Structure-building phenomena in systems with power-product forces



Part IX: Morphogenesis


E. Parisi (Institute of Molecular Embryology, Arco Felice, I-Naples); S. Filona (Institute of Histology and Embryology, University of Naples, I-Naples); A. Monroy (Zoological Station, I-Naples): Spatial-temporal coordination of mitotic activity in developing sear urchin embryos



Part X: Once again in chaos: theoretical approaches


R. Shaw (Physics Dept., University of California, Santa Cruz, CA 95064): Modeling chaotic systems


R.H.G. Helleman (Theoretical Physics, Twente University of Technology, NL-7500 AE Enschede): Feigenbaum sequences in conservative and dissipative systems


M. Diener (DŽpt. de Mathematiques, UniversitŽ dÕOran, Algeria); T. Poston (Institut fŸr Theoretische Physik, UniversitŠt Stuttgart, D-7000 Stuttgart): On the perfect delay convention, or the revolt of the slaved variables


W. Briggs, A.C. Newell, T. Sarie (Dept. of Mathematics and Computer Science, Clarkson College of Technology Potsdam, NY 13676): The mechanism by which many partial difference equations destabilize