Advanced Synergetics

1. Front Matter

   Pages I-XV

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2. Introduction

   • Hermann Haken

   Pages 1-60

3. Linear Ordinary Differential Equations

   • Hermann Haken

   Pages 61-102

4. Linear Ordinary Differential Equations with Quasiperiodic Coefficients

   • Hermann Haken

   Pages 103-142

5. Stochastic Nonlinear Differential Equations

   • Hermann Haken

   Pages 143-153

6. The World of Coupled Nonlinear Oscillators

   • Hermann Haken

   Pages 154-171

7. Nonlinear Coupling of Oscillators: The Case of Persistence of Quasiperiodic Motion

   • Hermann Haken

   Pages 172-186

8. Nonlinear Equations. The Slaving Principle

   • Hermann Haken

   Pages 187-221

9. Nonlinear Equations. Qualitative Macroscopic Changes

   • Hermann Haken

   Pages 222-266

10. Spatial Patterns

    • Hermann Haken

    Pages 267-281

11. The Inclusion of Noise

    • Hermann Haken

    Pages 282-302

12. Discrete Noisy Maps

    • Hermann Haken

    Pages 303-311

13. Example of an Unsolvable Problem in Dynamics

    • Hermann Haken

    Pages 312-313

14. Some Comments on the Relation Between Synergetics and Other Sciences

    • Hermann Haken

    Pages 314-316

15. Back Matter

    Pages 317-358

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This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con­ cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in­ dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man­ made. But we often forget that in many cases devices function by means of pro­ cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz­ ing systems and man-made devices is not at all rigid.

• Fourier series
• bifurcation
• chaos
• diffusion
• eigenvalue
• equilibrium
• geometry
• linear differential equation
• linear oscillation
• nonlinear differential equation
• path integral
• phase transition
• solution
• synergetics
• turbulence

• Institut für Theoretische Physik, Universität Stuttgart, Stuttgart 80, Fed. Rep. of Germany

  Hermann Haken

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