书名：Noise-induced phenomena in the environmental sciences
责任者：Luca Ridolfi | Paolo D Odorico | Francesco Laio.
ISBN\ISSN：9781108446785,1108446787,9780521198189,0521198186
出版时间：2011
出版社：Cambridge University Press,
分类号：一般工业技术
页数：xii, 313 p. :
前言
Randomness is ubiquitous in nature. Random drivers are generally considered a source of disorder in environmental systems. However, the interaction between noise and nonlinear dynamics may lead to the emergence of a number of ordered behaviors (in time and space) that would not exist in the absence of noise. This counterintuitive effect of randomness may play a crucial role in environmental processes. For example, seemingly 'random' background events in the atmosphere can grow into larger instabilities that have great effects on weather patterns. This book presents the basics of the theory of stochastic calculus and its application to the study of noise-induced phenomena in environmental systems. It will be an invaluable reference text for ecologists, geoscientists and environmental engineers interested in the study of stochastic environmental dynamics.
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目录
Preface page xi
1 Introduction 1
1.1 Noise-induced phenomena 1
1.2 Time scales and noise models 3
2 Noise-driven dynamical systems 7
2.1 Introduction 7
2.2 Dichotomous noise 7
2.2.1 Definition and properties 7
2.2.2 Dichotomous noise in the environmental sciences 11
2.2.3 Stochastic processes driven by dichotomous noise 14
2.3 White shot noise 28
2.3.1 Definition and properties 28
2.3.2 White shot noise as a limiting case of the DMN 30
2.3.3 Relevance of white shot noise in the biogeosciences 30
2.3.4 Stochastic process driven by white shot noise 31
2.4 White Gaussian noise 38
2.4.1 Definition and properties 38
2.4.2 White Gaussian noise as a limiting case of DMN and WSN 40
2.4.3 Relevance of Gaussian noise in the biogeosciences 40
2.4.4 Stochastic process driven by Gaussian noise 41
2.5 Colored Gaussian noise 44
2.5.1 Solution for linear Langevin equations 45
2.5.2 Dynamics driven by the Ornstein–Uhlenbeck process 46
3 Noise-induced phenomena in zero-dimensional systems 51
3.1 Introduction 51
3.2 Noise-induced transitions 51
3.2.1 Noise-induced transitions driven by dichotomous Markov noise 52
3.2.2 Noise-induced transitions for processes driven by shot noise 71
3.2.3 Noise-induced transitions for processes driven by Gaussian white noise 72
3.2.4 Noise-induced transitions for processes driven by Gaussian colored noise 76
3.3 Stochastic resonance 79
3.3.1 Basic concepts about stochastic resonance 79
3.3.2 Other forms of stochastic resonance 86
3.4 Coherence resonance 89
3.5 Noise-induced net transport 91
4 Noise-induced phenomena in environmental systems 98
4.1 Introduction 98
4.2 Dichotomous Markov noise in ecosystem dynamics 99
4.2.1 Noise-induced transitions due to random alternations between stressed and unstressed conditions in ecosystems 99
4.2.2 Noise-induced stability in dryland ecosystems 104
4.2.3 Noise-induced biodiversity 109
4.2.4 State-dependent dichotomous Markov noise in environmental systems 116
4.3 Environmental systems forced by white shot noise 117
4.3.1 Harvest process: Fire-induced tree–grass coexistence in savannas 118
4.3.2 Poisson harvest process with state-dependent harvest rate 121
4.3.3 Stochastic soil-mass balance 123
4.3.4 Stochastic soil-moisture dynamics 128
4.4 Environmental systems forced by Gaussian white noise 134
4.4.1 Harvest process driven by Gaussian white noise 134
4.4.2 Stochastic genetic model 135
4.4.3 Noise-induced extinction 138
4.4.4 Noise-induced bistability in climate dynamics: Effect of land–atmosphere interactions 142
4.5 Environmental systems forced by colored Gaussian noise 144
4.6 Environmental systems forced by other types of noise 146
4.7 Noise-induced phenomena in multivariate systems 147
4.7.1 Stochastic dynamics of two competing species 148
4.7.2 Phase transitions in multivariate systems driven by dichotomous noise 150
4.7.3 Stability of multivariate ecological systems with random interspecies interactions 154
4.8 Stochastic resonance and coherence in environmental processes 156
4.8.1 The Benzi–Parisi–Sutera–Vulpiani climate-change model 156
4.8.2 Fluctuations in the glacial climate: An effect of stochastic or coherence resonance? 159
4.8.3 A coherence-resonance mechanism of biodiversity 161
4.8.4 Coherence resonance in excitable predator–prey systems 163
5 Noise-induced pattern formation 167
5.1 Introduction 167
5.1.1 General aspects 167
5.1.2 Overview of stochastic mechanisms 171
5.1.3 Other noise-induced phenomena in spatiotemporal systems 182
5.1.4 Chapter organization 185
5.2 Additive noise and pattern-forming spatial couplings 186
5.2.1 Analysis of the deterministic dynamics 186
5.2.2 The role of the additive noise 189
5.3 Additive noise and non-pattern-forming spatial couplings 193
5.4 Multiplicative noise and pattern-forming spatial couplings 195
5.4.1 Prototype model 197
5.4.2 The effect of nonlinear g(φ) terms 203
5.4.3 Case with g(φ0) = 0: The van den Broeck–Parrondo–Toral model 205
5.5 Multiplicative noise and non-pattern-forming spatial couplings 210
5.5.1 The VPT model with diffusive spatial coupling 214
5.6 The role of the temporal autocorrelation of noise 216
5.7 Patterns accompanied by temporal phase transitions 219
5.7.1 Prototype model 220
5.7.2 Prototype model with non-pattern-forming coupling 224
5.7.3 A case with g(φ0) = 0 224
5.7.4 A particular subclass of processes 227
5.8 Patterns induced by periodic or random switching between deterministic dynamics 229
5.9 Spatiotemporal stochastic resonance 232
5.10 Spatiotemporal stochastic coherence 236
6 Noise-induced patterns in environmental systems 240
6.1 Introduction 240
6.2 Models of spatial interactions 243
6.3 Examples of pattern-forming processes 244
6.4 Patterns induced by additive noise 248
6.5 Patterns induced by multiplicative white shot noise 252
6.6 Random switching between two deterministic dynamics 256
6.6.1 Swift–Hohenberg process driven by dichotomous noise 256
6.6.2 Random switching between stressed and unstressed conditions in vegetation 259
6.7 Spatiotemporal stochastic resonance in predator–prey systems 265
6.8 Spatiotemporal coherence resonance in excitable plankton systems 266
Appendix A: Power spectrum and correlation 269
Appendix B: Deterministic mechanisms of pattern formation 274
B.1 Introduction 274
B.2 Turing-like instability 275
B.2.1 An example of a Turing model 278
B.3 Kernel-based models of spatial interactions 280
B.3.1 Biharmonic approximation of neural models 284
B.4 Patterns emerging from differential-flow instability 284
B.4.1 Case study: A differential-flow ecological model of pattern formation 286
Appendix C: List of symbols and acronyms 289
C.1 Greek symbols 289
C.2 Latin symbols 290
C.3 Mathematical symbols 291
C.4 Acronyms 291
Bibliography 293
Index 311
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作者简介
Luca Ridolfi is professor and director of the Department of Hydraulics and Fluid Dynamics at Politecnico di Torino. He is the author or co-author of about 100 peer-reviewed articles in ecohydrology, fluvial morphodynamics and bio-geography, river water quality and hydrodynamic instabilities. He is co-author of the book Generalized Collocation Methods: Solutions to Nonlinear Problems (2008). His research areas are in environmental fluid mechanics and ecohydrology. PA\Paolo D'Odorico is associate professor in the Department of Environmental Sciences at the University of Virginia. He is author or co-author of about ninety peer-reviewed articles in ecohydrology, soil moisture dynamics, global environmental change and desertification. He is editor of the book Dryland Ecohydrology (2006). His research areas are in hydrology and the environmental sciences. PA\Francesco Laio is assistant professor in the Department of Hydrology at Politecnico di Torino. He is author or co-author of about sixty peer-reviewed research articles in ecohydrology, stochastic hydrology and surface water hydrology. His research areas are hydrology, stochastic processes and statistics.
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