Bifurcation and Chaos: Analysis, Algorithms, Applications

1. Front Matter

   Pages I-X

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2. A Complete Bifurcation Scenario for the 2-d Nonlinear Laplacian with Neumann Boundary Conditions on the Unit Square

   • Eugene L. Allgower, Klaus Böhmer, Mei Zhen

   Pages 1-18

3. The Effect of Fluctuations on the Transition Behavior of a Nonlinear Chemical Oscillator

   • J. Amrehn, Th.-M. Kruel, F. W. Schneider, F. Buchholtz

   Pages 19-25

4. Examples of Boundary Crisis Phenomenon in Structural Dynamics

   • A. K. Bajaj

   Pages 27-36

5. Bifurcation, Pattern Formation, and Transition to Chaos in Combustion

   • A. Bayliss, B. J. Matkowsky

   Pages 37-52

6. On the Primary and Secondary Bifurcation of Equations Involving Scalar Nonlinearities

   • N. W. Bazley, N. X. Tan

   Pages 53-57

7. Periodic Solutions Leading to Chaos in an Oscillator with Quadratic and Cubic Nonlinearities

   • F. Benedettini, G. Rega

   Pages 59-65

8. Turing Structures in Anisotropic Media

   • J. Boissonade, V. Castets, E. Dulos, P. De Kepper

   Pages 67-77

9. Regular and Chaotic Patterns of Rayleigh-Benard Convection

   • F. H. Busse, M. Sieber

   Pages 79-92

10. Bifurcations in slowly rotating systems with spherical geometry

    • G. Dangelmayr, C. Geiger

    Pages 93-97

11. An Elastic Model with Continuous Spectrum

    • Domokos Gábor

    Pages 99-103

12. Mechanistic Requirements for Chemical Oscillations

    • M. Eiswirth, A. Freund, J. Ross

    Pages 105-109

13. Envelope Soliton Chaos Model for Mechanical System

    • M. S. El Naschie, T. Kapitaniak

    Pages 111-115

14. Rolling Motion of Ships Treated as Bifurcation Problem

    • J. Falzarano, A. Steindl, A. Troesch, H. Troger

    Pages 117-121

15. Normal Forms for Planar Systems With Nilpotent Linear Part

    • E. Gamero, E. Freire, E. Ponce

    Pages 123-127

16. Two Methods for the Numerical Detection of Hopf Bifurcations

    • T. J. Garratt, G. Moore, A. Spence

    Pages 129-133

17. Automatic Evaluation of First and Higher-Derivative Vectors

    • Andreas Griewank

    Pages 135-148

18. On the Stability of a Spinning Satellite in a Central Force Field

    • Ardéshir Guran

    Pages 149-153

19. Codimension Two Bifurcation in an Approximate Model for Delayed Robot Control

    • G. Haller, G. Stépán

    Pages 155-159

20. Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems

    • Hans-Peter Heinz

    Pages 161-169

This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap­ plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen­ cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti­ cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art.

• Eigenvalue
• Laplace operator
• Volume
• bifurcation
• derivative
• differential equation
• distribution
• dynamical systems
• manifold
• maximum
• minimum
• numerical method
• ordinary differential equation
• partial differential equation
• stability

• Abteilung für Numerik, Universität Ulm, Ulm, Germany

  R. Seydel

• Institut für Physikalische Chemie, Universität Würzburg, Würzburg, Germany

  F. W. Schneider

• Mathematisches Institut, Universität Köln, Köln, Germany

  T. Küpper

• Institut für Mechanik, Technische Universität Wien, Wien, Austria

  H. Troger

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