Stochastic Nonlinear Systems in Physics, Chemistry, and Biology

1. Front Matter

   Pages I-VIII

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2. Introduction: From Deterministic to Stochastic Behavior

   1. Front Matter

      Pages 1-1

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   2. On the Foundations of Kinetic Theory

      • B. Misra, I. Prigogine

      Pages 2-11

   3. Transition Phenomena in Nonlinear Systems

      • H. Haken

      Pages 12-19

3. Approximation of Stochastic Processes

   1. Front Matter

      Pages 21-21

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   2. Approximation of Discontinuous Processes by Continuous Processes

      • Thomas G. Kurtz

      Pages 22-35

   3. On the Asymptotic Behavior of Motions in Random Flows

      • G. Papanicolaou, O. Pironeau

      Pages 36-41

4. Description of Internal Fluctuations

   1. Front Matter

      Pages 43-43

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   2. Some Aspects of Fluctuation Theory in Nonequilibrium Systems

      • G. Nicolis

      Pages 44-52

   3. Aspects of Classical and Quantum Theory of Stochastic Bistable Systems

      • C. W. Gardiner

      Pages 53-61

   4. Kinetics of Phase Separation

      • Kurt Binder

      Pages 62-71

   5. Chemical Instabilities and Broken Symmetry: The Hard Mode Case

      • D. Walgraef, G. Dewel, P. Borckmans

      Pages 72-83

5. Long-Term Behavior of Stochastic Systems

   1. Front Matter

      Pages 85-85

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   2. Asymptotic Behavior of Several Dimensional Diffusions

      • R. N. Bhattacharya

      Pages 86-99

   3. Qualitative Theory of Stochastic Non-Linear Systems

      • Ludwig Arnold

      Pages 100-113

6. External Fluctuations and Noise Induced Transitions

   1. Front Matter

      Pages 115-115

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   2. Noise Induced Transitions

      • Werner Horsthemke

      Pages 116-126

   3. Noise Induced Transitions in Biological Systems

      • René Lefever

      Pages 127-136

   4. Multiplicative Ornstein Uhlenbeck Noise in Nonequilibrium Phenomena

      • M. San Miguel, J. M. Sancho

      Pages 137-150

7. Stochastic Behavior in Model Systems

   1. Front Matter

      Pages 151-151

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This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch­ astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se­ ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. .

• Biology
• Chemistry
• Nichtlineares System
• Physics
• Stochastic processes
• Stochastisches System
• System
• Systems
• stochastic process
• thermodynamics

• Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bremen 33, Fed. Rep. of Germany

  Ludwig Arnold

• Service de Chemie Physique II, Université Libre de Bruxelles, Bruxelles, Belgium

  René Lefever

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