Noise Sustained Patterns

The following sections are included:

• Preface

• Acknowledgements

• Contents

The following sections are included:

• Stability theory revisited
  • Noise and metastability
  • Linear stability analysis

• Instabilities and nonlinear events in everyday life
  • Arms race
  • Distribution of wealth
  • Front nucleation and propagation
  • Supply chain dynamics
  • A hodgepodge of mechanical instabilities

• Postscript

The following sections are included:

• Probabilistic and information theoretic measures

• Matrix manipulations
  • Circulant matrices
  • Singular value decomposition

• Delay-differential equations

• The fluctuation-dissipation theorem

• The Fokker-Planck equation

• Numerical techniques for the simulation of stochastic equations

• Experimental aspects of generating noise

• Complex integration

The following sections are included:

• Escape from metastable states

• Stochastic resonance in bistable systems
  • Double-well potential
  • Two state theory
  • The diode resonator
  • The logistic map

• Postscript

The following sections are included:

• Spatiotemporal stochastic resonance
  • Array enhancement
  • Global vs. local dynamics
  • Kink nucleation in a ϕ⁴ model
  • Kink nucleation in the experiment
  • Decay rates and kink speeds
  • Coupled maps

• Doubly stochastic resonance

• Spatial patterns
  • Parametric surface waves
    • Noise induced bistability of Faraday waves
    • Granular flow
    • Intermittent pattern switching

• Postscript

The following sections are included:

• Noise-sustained structures in convectively unstable media
  • The Ginzburg-Landau equation
  • Unidirectionally coupled diode resonators
  • Coupled maps

• Noise sustained front transmission
  • Propagation failure in cardiac tissue
  • Information theoretic measures revisited: ROC curves

• Theory
  • The continuum limit
  • Kink Brownian motion
  • The Peierls-Nabarro potential

• Noise enhanced wave propagation
  • Monostable noise enhanced propagation

• Stochastic ratchets and Brownian motors

• Postscript

The following sections are included:

• Minority game
  • The thermal minority game

• Traffic dynamics
  • Time-continuous model
  • Discrete time dynamics

• Dithering

• Noise in neural networks

Arriving at the "conclusion" is always a difficult and probing instant in the course of both reading and writing a book. The author faces the peril of questioning and doubting the consistency, completeness and uniformity of the just presented, necessarily narrow excerpt of a field as wide as stochastic phenomena. As with many personal works, at this point the temptation to "start all over" and rewrite entire chapters is at its greatest. The reader, on the other hand, is likely looking for guidance on how to most efficiently digest the huge amount of information already absorbed. The main challenge for the author is therefore to concentrate on simple lessons learned and to propose unsolved problems…

The following sections are included:

• Appendix A Normal Matrices

• Appendix B Integrating Colored-Noise, Coupled SDEs
  • Exploiting symmetries of coupled differential equations
  • Coupled Duffing oscillators

• Appendix C Numerical Implementation of the FFT

• Appendix D Absolute and Convective Instabilities

• Bibliography

• Index