非线性时间序列分析 第2版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

非线性时间序列分析 第2版 英文PDF格式电子书版下载

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Ⅰ Basic topics1

1 Introduction:why nonlinear methods?3

2 Linear tools and general considerations13

2.1 Stationarity and sampling13

2.2 Testing for stationarity15

2.3 Linear correlations and the power spectrum18

2.3.1 Stationarity and the low-frequency component in the power spectrum23

2.4 Linear filters24

2.5 Linear predictions27

3 Phase space methods30

3.1 Determinism:uniqueness in phase space30

3.2 Delay reconstruction35

3.3 Finding a good embedding36

3.3.1 False neighbours37

3.3.2 The time lag39

3.4 Visual inspection of data39

3.5 Poincaré surface of section41

3.6 Recurrence plots43

4 Determinism and predictability48

4.1 Sources of predictability48

4.2 Simple nonlinear prediction algorithm50

4.3 Verification of successful prediction53

4.4 Cross-prediction errors:probing stationarity56

4.5 Simple nonlinear noise reduction58

5 Instability:Lyapunov exponents65

5.1 Sensitive dependence on initial conditions65

5.2 Exponential divergence66

5.3 Measuring the maximal exponent from data69

6 Self-similarity:dimensions75

6.1 Attractor geometry and fractals75

6.2 Correlation dimension77

6.3 Correlation sum from a time series78

6.4 Interpretation and pitfalls82

6.5 Temporal correlations,non-stationarity,and space time separation plots87

6.6 Practical considerations91

6.7 A useful application:determination of the noise level using the correlation integral92

6.8 Multi-scale or self-similar signals95

6.8.1 Scaling laws96

6.8.2 Detrended fluctuation analysis100

7 Using nonlinear methods when determinism is weak105

7.1 Testing for nonlinearity with surrogate data107

7.1.1 The null hypothesis109

7.1.2 How to make surrogate data sets110

7.1.3 Which statistics to use113

7.1.4 What can go wrong115

7.1.5 What we have learned117

7.2 Nonlinear statistics for system discrimination118

7.3 Extracting qualitative information from a time series121

8 Selected nonlinear phenomena126

8.1 Robustness and limit cycles126

8.2 Coexistence of attractors128

8.3 Transients128

8.4 Intermittency129

8.5 Structural stability133

8.6 Bifurcations135

8.7 Quasi-periodicity139

Ⅱ Advanced topics141

9 Advanced embedding methods143

9.1 Embedding theorems143

9.1.1 Whitney's embedding theorem144

9.1.2 Takens's delay embedding theorem146

9.2 The time lag148

9.3 Filtered delay embeddings152

9.3.1 Derivative coordinates152

9.3.2 Principal component analysis154

9.4 Fluctuating time intervals158

9.5 Multichannel measurements159

9.5.1 Equivalent variables at different positions160

9.5.2 Variables with different physical meanings161

9.5.3 Distributed systems161

9.6 Embedding of interspike intervals162

9.7 High dimensional chaos and the limitations of the time delay embedding165

9.8 Embedding for systems with time delayed feedback171

10 Chaotic data and noise174

10.1 Measurement noise and dynamical noise174

10.2 Effects of noise175

10.3 Nonlinear noise reduction178

10.3.1 Noise reduction by gradient descent179

10.3.2 Local projective noise reduction180

10.3.3 Implementation of locally projective noise reduction183

10.3.4 How much noise is taken out?186

10.3.5 Consistency tests191

10.4 An application:foetal ECG extraction193

11 More about invariant quantities197

11.1 Ergodicity and strange attractors197

11.2 Lyapunov exponents Ⅱ199

11.2.1 The spectrum of Lyapunov exponents and invariant manifolds200

11.2.2 Flows versus maps202

11.2.3 Tangent space method203

11.2.4 Spurious exponents205

11.2.5 Almost two dimensional flows211

11.3 Dimensions Ⅱ212

11.3.1 Generalised dimensions,multi-fractals213

11.3.2 Information dimension from a time series215

11.4 Entropies217

11.4.1 Chaos and the flow of information217

11.4.2 Entropies of a static distribution218

11.4.3 The Kolmogorov-Sinai entropy220

11.4.4 The ∈-entropy per unit time222

11.4.5 Entropies from time series data226

11.5 How things are related229

11.5.1 Pesin's identity229

11.5.2 Kaplan-Yorke conjecture231

12 Modelling and forecasting234

12.1 Linear stochastic models and filters236

12.1.1 Linear filters237

12.1.2 Nonlinear filters239

12.2 Deterministic dynamics240

12.3 Local methods in phase space241

12.3.1 Almost model free methods241

12.3.2 Local linear fits242

12.4 Global nonlinear models244

12.4.1 Polynomials244

12.4.2 Radial basis functions245

12.4.3 Neural networks246

12.4.4 What to do in practice248

12.5 Improved cost functions249

12.5.1 Overfitting and model costs249

12.5.2 The errors-in-variables problem251

12.5.3 Modelling versus prediction253

12.6 Model verification253

12.7 Nonlinear stochastic processes from data256

12.7.1 Fokker—Planck equations from data257

12.7.2 Markov chains in embedding space259

12.7.3 No embedding theorem for Markov chains260

12.7.4 Predictions for Markov chain data261

12.7.5 Modelling Markov chain data262

12.7.6 Choosing embedding parameters for Markov chains263

12.7.7 Application:prediction of surface wind velocities264

12.8 Predicting prediction errors267

12.8.1 Predictability map267

12.8.2 Individual error prediction268

12.9 Multi-step predictions versus iterated one-step predictions271

13 Non-stationary signals275

13.1 Detecting non-stationarity276

13.1.1 Making non-stationary data stationary279

13.2 Over-embedding280

13.2.1 Deterministic systems with parameter drift280

13.2.2 Markov chain with parameter drift281

13.2.3 Data analysis in over-embedding spaces283

13.2.4 Application:noise reduction for human voice286

13.3 Parameter spaces from data288

14 Coupling and synchronisation of nonlinear systems292

14.1 Measures for interdependence292

14.2 Transfer entropy297

14.3 Synchronisation299

15 Chaos control304

15.1 Unstable periodic orbits and their invariant manifolds306

15.1.1 Locating periodic orbits306

15.1.2 Stable/unstable manifolds from data312

15.2 OGY-control and derivates313

15.3 Variants of OGY-control316

15.4 Delayed feedback317

15.5 Tracking318

15.6 Related aspects319

A Using the TISEAN programs321

A.1 Information relevant to most of the routines322

A.1.1 Efficient neighbour searching322

A.1.2 Re-occurring command options325

A.2 Second-order statistics and linear models326

A.3 Phase space tools327

A.4 Prediction and modelling329

A.4.1 Locally constant predictor329

A.4.2 Locally linear prediction329

A.4.3 Global nonlinear models330

A.5 Lyapunov exponents331

A.6 Dimensions and entropies331

A.6.1 The correlation sum331

A.6.2 Information dimension,fixed mass algorithm332

A.6.3 Entropies333

A.7 Surrogate data and test statistics334

A.8 Noise reduction335

A.9 Finding unstable periodic orbits336

A.10 Multivariate data336

B Description of the experimental data sets338

B.1 Lorenz-like chaos in an NH3 laser338

B.2 Chaos in a periodically modulated NMR laser340

B.3 Vibrating string342

B.4 Taylor-Couette flow342

B.5 Multichannel physiological data343

B.6 Heart rate during atrial fibrillation343

B.7 Human electrocardiogram(ECG)344

B.8 Phonation data345

B.9 Postural control data345

B.10 Autonomous CO2 laser with feedback345

B.11 Nonlinear electric resonance circuit346

B.12 Frequency doubling solid state laser348

B.13 Surface wind velocities349

References350

Index365