Noise-Induced Phenomena in the Environmental Sciences

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1.1 Noise-induced phenomena......Page 15
1.2 Time scales and noise models......Page 17
2.2.1 Definition and properties......Page 21
2.2.2 Dichotomous noise in the environmental sciences......Page 25
2.2.3.1 General framework......Page 28
2.2.3.2 Derivation of the steady-state probability density function......Page 30
2.2.3.3 Domain of the steady-state probability distribution......Page 34
2.2.3.4 Behavior of the steady-state pdf at the boundaries......Page 38
2.2.3.5 State-dependent DMN......Page 39
2.3.1 Definition and properties......Page 42
2.3.3 Relevance of white shot noise in the biogeosciences......Page 44
2.3.4 Stochastic process driven by white shot noise......Page 45
2.3.4.2 Steady-state pdf and its properties......Page 48
2.4.1 Definition and properties......Page 52
2.4.3 Relevance of Gaussian noise in the biogeosciences......Page 54
2.4.4.1 Some examples of processes driven by Gaussian white noise......Page 55
2.4.4.2 Steady-state pdf and its properties......Page 56
2.5 Colored Gaussian noise......Page 58
2.5.1 Solution for linear Langevin equations......Page 59
2.5.2 Dynamics driven by the Ornstein–Uhlenbeck process......Page 60
3.2 Noise-induced transitions......Page 65
3.2.1 Noise-induced transitions driven by dichotomous Markov noise......Page 66
3.2.1.1 Noise-induced transitions for processes driven by additive DMN......Page 69
3.2.1.2 Noise-induced transitions for processes driven by multiplicative DMN......Page 74
3.2.1.3 Periodic forcing as a term of comparison......Page 75
3.2.1.4 Noise-induced transitions driven by dichotomous noise with feedback......Page 80
3.2.2 Noise-induced transitions for processes driven by shot noise......Page 85
3.2.3 Noise-induced transitions for processes driven by Gaussian white noise......Page 86
3.2.4 Noise-induced transitions for processes driven by Gaussian colored noise......Page 90
3.3.1 Basic concepts about stochastic resonance......Page 93
3.3.2 Other forms of stochastic resonance......Page 100
3.4 Coherence resonance......Page 103
3.5 Noise-induced net transport......Page 105
4.1 Introduction......Page 112
4.2.1 Noise-induced transitions due to random alternations between stressed and unstressed conditions in ecosystems......Page 113
4.2.2 Noise-induced stability in dryland ecosystems......Page 118
4.2.3 Noise-induced biodiversity......Page 123
4.2.4 State-dependent dichotomous Markov noise in environmental systems......Page 130
4.3 Environmental systems forced by white shot noise......Page 131
4.3.1 Harvest process: Fire-induced tree–grass coexistence in savannas......Page 132
4.3.2 Poisson harvest process with state-dependent harvest rate......Page 135
4.3.3 Stochastic soil-mass balance......Page 137
4.3.4 Stochastic soil-moisture dynamics......Page 142
4.4.1 Harvest process driven by Gaussian white noise......Page 148
4.4.2 Stochastic genetic model......Page 149
4.4.3 Noise-induced extinction......Page 152
4.4.4 Noise-induced bistability in climate dynamics: Effect of land–atmosphere interactions......Page 156
4.5 Environmental systems forced by colored Gaussian noise......Page 158
4.6 Environmental systems forced by other types of noise......Page 160
4.7 Noise-induced phenomena in multivariate systems......Page 161
4.7.1 Stochastic dynamics of two competing species......Page 162
4.7.2 Phase transitions in multivariate systems driven by dichotomous noise......Page 164
4.7.3 Stability of multivariate ecological systems with random interspecies interactions......Page 168
4.8.1 The Benzi–Parisi–Sutera–Vulpiani climate-change model......Page 170
4.8.2 Fluctuations in the glacial climate: An effect of stochastic or coherence resonance?......Page 173
4.8.3 A coherence-resonance mechanism of biodiversity......Page 175
4.8.4 Coherence resonance in excitable predator–prey systems......Page 177
5.1.1 General aspects......Page 181
5.1.2 Overview of stochastic mechanisms......Page 185
5.1.2.1 Models of the noise term......Page 186
5.1.2.2 Models of spatial coupling......Page 187
5.1.2.3 Prognostic tools for pattern detection......Page 189
5.1.2.4 Numerical simulation of random fields......Page 193
5.1.3 Other noise-induced phenomena in spatiotemporal systems......Page 196
5.1.4 Chapter organization......Page 199
5.2.1 Analysis of the deterministic dynamics......Page 200
5.2.2 The role of the additive noise......Page 203
5.3 Additive noise and non-pattern-forming spatial couplings......Page 207
5.4 Multiplicative noise and pattern-forming spatial couplings......Page 209
5.4.1 Prototype model......Page 211
5.4.2 The effect of nonlinear g(phi) terms......Page 217
5.4.3 Case with … The van den Broeck–Parrondo–Toral model......Page 219
5.5 Multiplicative noise and non-pattern-forming spatial couplings......Page 224
5.5.1 The VPT model with diffusive spatial coupling......Page 228
5.6 The role of the temporal autocorrelation of noise......Page 230
5.7 Patterns accompanied by temporal phase transitions......Page 233
5.7.1 Prototype model......Page 234
5.7.3 A case with g(phi0)=0......Page 238
5.7.4 A particular subclass of processes......Page 241
5.8 Patterns induced by periodic or random switching between deterministic dynamics......Page 243
5.9 Spatiotemporal stochastic resonance......Page 246
5.10 Spatiotemporal stochastic coherence......Page 250
6.1 Introduction......Page 254
6.2 Models of spatial interactions......Page 257
6.3 Examples of pattern-forming processes......Page 258
6.4 Patterns induced by additive noise......Page 262
6.5 Patterns induced by multiplicative white shot noise......Page 266
6.6.1 Swift–Hohenberg process driven by dichotomous noise......Page 270
6.6.2 Random switching between stressed and unstressed conditions in vegetation......Page 273
6.7 Spatiotemporal stochastic resonance in predator–prey systems......Page 279
6.8 Spatiotemporal coherence resonance in excitable plankton systems......Page 280
Appendix A: Power spectrum and correlation......Page 283
B.1 Introduction......Page 288
B.2 Turing-like instability......Page 289
B.2.1 An example of a Turing model......Page 292
B.3 Kernel-based models of spatial interactions......Page 294
B.4 Patterns emerging from differential-flow instability......Page 298
B.4.1 Case study: A differential-flow ecological model of pattern formation......Page 300
C.1 Greek symbols......Page 303
C.2 Latin symbols......Page 304
C.4 Acronyms......Page 305
Bibliography......Page 307
Index......Page 325