Contents -- Preface -- Acknowledgements -- Chapter 1 Introduction -- 1.1 Stability theory revisited -- 1.1.1 Noise and metastability -- 1.1.2 Linear stability analysis -- 1.2 Instabilities and nonlinear events in everyday life -- 1.2.1 Arms race -- 1.2.2 Distribution of wealth -- 1.2.3 Front nucleation and propagation -- 1.2.4 Supply chain dynamics -- 1.2.5 A hodgepodge of mechanical instabilities -- 1.3 Postscript -- Chapter 2 Essentials -- 2.1 Probabilistic and information theoretic measures -- 2.2 Matrix manipulations -- 2.2.1 Circulant matrices -- 2.2.2 Singular value decomposition -- 2.3 Delay-differential equations -- 2.4 The fluctuation-dissipation theorem -- 2.5 The Fokker-Planck equation -- 2.6 Numerical techniques for the simulation of stochastic equations -- 2.7 Experimental aspects of generating noise -- 2.8 Complex integration -- Chapter 3 Noise Induced Temporal Phenomena -- 3.1 Escape from metastable states -- 3.2 Stochastic resonance in bistable systems -- 3.2.1 Double-well potential -- 3.2.2 Two state theory -- 3.2.3 The diode resonator -- 3.2.4 The logistic map -- 3.3 Postscript -- Chapter 4 Adding Spatial Dimensions -- 4.1 Spatiotemporal stochastic resonance -- 4.1.1 Array enhancement -- 4.1.2 Global vs. local dynamics -- 4.1.3 Kink nucleation in a O4 model -- 4.1.4 Kink nucleation in the experiment -- 4.1.5 Decay rates and kink speeds -- 4.1.6 Coupled maps -- 4.2 Doubly stochastic resonance -- 4.3 Spatial patterns -- 4.3.1 Parametric surface waves -- 4.4 Postscript -- Chapter 5 Stochastic Transport Phenomena -- 5.1 Noise-sustained structures in convectively unstable media -- 5.1.1 The Ginzburg-Landau equation -- 5.1.2 Unidirectionally coupled diode resonators -- 5.1.3 Coupled maps -- 5.2 Noise sustained front transmission -- 5.2.1 Propagation failure in cardiac tissue.

5.2.2 Information theoretic measures revisited: ROC curves -- 5.3 Theory -- 5.3.1 The continuum limit -- 5.3.2 Kink Brownian motion -- 5.3.3 The Peierls-Nabarro potential -- 5.4 Noise enhanced wave propagation -- 5.4.1 Monostable noise enhanced propagation -- 5.5 Stochastic ratchets and Brownian motors -- 5.6 Postscript -- Chapter 6 Sundry Topics -- 6.1 Minority game -- 6.1.1 The thermal minority game -- 6.2 Traffic dynamics -- 6.2.1 Time-continuous model -- 6.2.2 Discrete time dynamics -- 6.3 Dithering -- 6.4 Noise in neural networks -- Chapter 7 Afterthoughts -- Appendix A Normal Matrices -- Appendix B Integrating Colored-Noise Coupled SDEs -- B.l Exploiting symmetries of coupled differential equations -- B.2 Coupled Duffing oscillators -- Appendix C Numerical Implementation of the FPT -- Appendix D Absolute and Convective Instabilities -- Bibliography -- Index.