Reduction of Complexity by Optimal Driving Forces

  • Thomas Meyer
  • Alfred Hübler
  • Norman Packard
Part of the NATO ASI Series book series (NSSB, volume 208)


In general nonlinear waves are not stable in a chain of finite length. Since they have a finite lifetime, it is important to investigate the production of nonlinear waves, e.g. the production of solitons. A general feature of nonlinear waves is the amplitude frequency coupling, which causes the excitation by sinusoidal driving forces to be very inefficient. The response is usually very complex in addition. We present a method to calculate special aperiodic driving forces, which generates nonlinear waves very efficiently. The response to these driving forces is very simple.


Nonlinear Wave Nonlinear Oscillator Field Amplitude Sine Gordon Equation Chaotic State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Eisenhammer, A. Hübler, T. Geisel, E. Löscher, Scaling Behavior of the Maximum Energy Exchange between Coupled Anharmonic Oscillators, to be publishedGoogle Scholar
  2. T. Eisenhammer, T. Hecht, A. Hübler, E. Löscher, Skalengesetze für den maximalen Energieaustausch nichtlinearer gekoppelter Systeme, Naturwissenschaften 74: 336 (1987)CrossRefGoogle Scholar
  3. 2.
    T.F. Hueter and R.H. Bolt,“Sonics”,John Wiley amp; Sons, New York 1966, 5th ed., p.20Google Scholar
  4. 3.
    D. Ruelle, Resonances of Chaotic Dynamical Systems, Phys.Rev.Lett. 56: 405 (1986)MathSciNetCrossRefGoogle Scholar
  5. U. Parlitz and W. Lauterborn, Superstructure in the Bifurcation Set of the Duffing Equation, Phys.Lett. 107A: 351 (1985)MathSciNetCrossRefGoogle Scholar
  6. 4.
    B.A. Huberman and J.P. Crutchfield, Chaotic States of Anharmonic Systems in Periodic Fields, Phys.Rev.Lett. 43: 1743 (1979)CrossRefGoogle Scholar
  7. D.D. Humieres, M.R. Beasley, B.A. Huberman, and A. Libchaber, Chaotic States and Routes to Chaos in the Forced Pendulum, Phys.Rev.A 26: 3483 (1982)CrossRefGoogle Scholar
  8. 5.
    A. Hübler, E. Löscher, Resonant stimulation and control of complex systems, Helv.Phys.Acta 61: (1989)Google Scholar
  9. 6.
    A. Hübler, E. Löscher, Resonant stimulation and control of nonlinear oscillators, Naturwissenschaften 76: 67 (1989)CrossRefGoogle Scholar
  10. 7.
    R.K. Bullough and P.J. Caudrey eds., “Solitons”, Springer, Berlin 1980zbMATHGoogle Scholar
  11. A.S. Davydov, “Solitons in molecular systems”, D.Reindel, Dordrecht (1985)zbMATHGoogle Scholar
  12. S. Takeno, “Dynamical Problems in Soliton Systems”, Springer Series in Synergetics, Springer, Berlin (1985)zbMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Thomas Meyer
    • 1
  • Alfred Hübler
    • 1
  • Norman Packard
    • 1
  1. 1.Department of Physics Beckman InstituteCenter for Complex Systems ResearchUrbanaUSA

Personalised recommendations