## Synergetics: An Introduction Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and BiologyThe publication of this second edition was motivated by several facts. First of all, the first edition had been sold out in less than one year. It had found excellent critics and enthusiastic responses from professors and students welcoming this new interdisciplinary approach. This appreciation is reflected by the fact that the book is presently translated into Russian and Japanese also. I have used this opportunity to include some of the most interesting recent developments. Therefore I have added a whole new chapter on the fascinating and rapidly growing field of chaos dealing with irregular motion caused by deterministic forces. This kind of phenomenon is presently found in quite diverse fields ranging from physics to biology. Furthermore I have included a section on the analytical treatment of a morphogenetic model using the order parameter concept developed in this book. Among the further additions, there is now a complete description of the onset of ultrashort laser pulses. It goes without· saying that the few minor mis prints or errors of the first edition have been corrected. I wish to thank all who have helped me to incorporate these additions. |

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### Contents

1 | |

Chance | 16 |

Necessity | 104 |

17 | 108 |

Chance and Necessity | 146 |

SelfOrganization | 191 |

Physical Systems | 224 |

Chemical and Biochemical Systems | 263 |

7+ Stochastic Treatment of the Brusselator Close to Its SoftMode | 286 |

Applications to Biology | 293 |

A Stochastic Model for the Formation of Public Opinion | 315 |

Some Historical Remarks and Outlook | 333 |

350 | |

### Other editions - View all

Synergetics: An Introduction : Nonequilibrium Phase Transitions ..., Volume 2 Hermann Haken No preview available - 1978 |

### Common terms and phrases

6-function abbreviation adiabatic adiabatic elimination amplitude analogy assume atoms becomes unstable behavior cells chapter chemical reactions coefficients compare Fig condition consider constant coordinate correlation function corresponding damped defined denote density depends derive described detailed balance determined differential diffusion discuss distribution function energy entropy evaluate example Exercise fluctuating forces fluid Fokker-Planck equation Furthermore Gaussian given Haken information entropy initial Inserting integral introduce inversion joint probability Langevin equation laser limit cycle linear Ljapunov Lorenz model macroscopic master equation mathematical means mechanics molecules morphogenesis nonlinear obtain occurs order parameter oscillator particle phase transition Phys physics potential curve probability distribution problem procedure quantities random variables replace Sect Section self-organization spatial stable stationary solution stochastic subsystems symmetry Synergetics temperature temporal theory thermal equilibrium thermodynamics time-dependent tion trajectories treat unstable modes values vector velocity yields