非線性時間序列分析

定　價：￥39.00

作　者：	（英）Holger Kantz，（英）Thomas Schreiber著
出版社：	清華大學(xué)出版社
叢編項(xiàng)：	劍橋非線性科學(xué)系列
標(biāo)　簽：	非線性

購買這本書可以去

ISBN：	9787302039068	出版時間：	2001-01-01	包裝：	精裝
開本：	26cm	頁數(shù)：	304頁	字?jǐn)?shù)：

內(nèi)容簡介

　　Deterministic chaos offers a striking explanation for irregular behaviour and anomalies in systems which do not seem to＇ be inherently stochastic. The most direct link between chaos theory and the rea

作者簡介

暫缺《非線性時間序列分析》作者簡介

圖書目錄

PrefaceVii
AcknowledgementsiX
Part1BasictopicsI
Chapter1Introduction:Whynonlinearmethods?3
Chapter2Lineartoolsandgeneralconsiderations13
2.1Stationarityandsampling13
2.2Testingforstationarity15
2.3Linearcorrelationsandthepowerspectrum18
2.3.1Stationarityandthelow-frequencycomponentinthepowerspectrum22
2.4Linearfilters23
2.5Linearpredictions25
Chapter3Phasespacemethods29
3.1Determinism:Uniquenessinphasespace29
3.2Delayreconstruction33
3.3Findingagoodembedding34
3.4Visualinspectionofdata37
3.5Poincaresurfaceofsection37
Chapter4Determinismandpredictability42
4.1Sourcesofpredictability43
4.2Simplenonlinearpredictionalgorithm44
4.3Verificationofsuccessfulprediction46
4.4Probingstationaritywithnonlinearpredictions49
4.5Simplenonlinearnoisereduction51
Chapter5Instability:Lyapunovexponents58
5.1Sensitivedependenceoninitialconditions58
5.2Exponentialdivergence59
5.3Measuringthemaximalexponentfromdata62
Chapter6Self-similarity:Dimensions69
6.1Attractorgeometryandfractals69
6.2Correlationdimension70
6.3Correlationsumfromatimeseries72
6.4Interpretationandpitfalls75
6.5Temporalcorrelations,nonstationarity,andspacetimeseparationplots81
6.6Practicalconsiderations84
6.7Ausefulapplication:Determinationofthenoiselevel86
Chapter7Usingnonlinearmethodswhendeterminismisweak91
7.1Testingfornonlinearitywithsurrogatedata93
7.1.1Thenullhypothesis95
7.1.2Howtomakesurrogatedatasets96
7.1.3Whichstatisticstouse99
7.1.4Whatcangowrong102
7.1.5Whatwehavelearned103
7.2Nonlinearstatisticsforsystemdiscrimination104
7.3Extractingqualitativeinformationfromatimeseries108
Chapter8Selectednonlinearphenomena112
8.1Coexistenceofattractors112
8.2Transients113
8.3Intermittency114
8.4Structuralstability118
8.5Bifurcations119
8.6Quasi-periodicity121
Part2Advancedtopics123
Chapter9Advancedembeddingmethods125
9.1Embeddingtheorems125
9.1.1Whitney'sembeddingtheorem126
9.1.2Takens'sdelayembeddingtheorem127
9.2Thetimelag130
9.3Filtereddelayembeddings134
9.3.1Derivativecoordinates134
9.3.2Principalcomponentanalysis135
9.4Fluctuatingtimeintervals139
9.5Multichannelmeasurements141
9.5.1Equivalentvariablesatdifferentpositions141
9.5.2Variableswithdifferentphysicalmeanings142
9.5.3Distributedsystems143
9.6Embeddingofinterspikeintervals145
Chapter10Chaoticdataandnoise150
10.1Measurementnoiseanddynamicalnoise150
10.2Effectsofnoise151
10.3Nonlinearnoisereduction154
10.3.1Noisereductionbygradientdescent155
10.3.2Localprojectivenoisereduction156
10.3.3Implementationoflocallyprojectivenoisereduction159
10.3.4Howmuchnoiseistakenout?163
10.3.5Consistencytests167
10.4Anapplication:FoetalECGextraction168
Chapter11Moreaboutinvariantqnantities172
11.1Ergodicityandstrangeattractors173
11.2LyapunovexponentsII174
11.2.1ThespectrumofLyapunovexponentsandinvariantmanifolds174
11.2.2Flowsversusmaps176
11.2.3Tangentspacemethod177
11.2.4Spuriousexponents178
11.2.5Almosttwo-dimensionalflows184
11.3DimensionsII184
11.3.1Generaliseddimensions,multifractals186
11.3.2Informationdimensionfromatimeseries188
11.4Entropies189
11.4.1Chaosandtheflowofinformation189
11.4.2Entropiesofastaticdistribution191
11.4.3TheKolmogorov-Sinaientropy193
11.4.4Entropiesfromtimeseriesdata194
11.5Howthingsarerelated198
11.5.1Pesin'sidentity198
11.5.2Kaplan-Yorkeconjecture199
Chapter12Modellingandforecasting202
12.1Stochasticmodels204
12.1.1Linearfilters204
12.1.2Nonlinearfilters206
12.1.3Markermodels207
12.2Deterministicdynamics207
12.3Localmethodsinphasespace208
12.3.1Almostmodelfreemethods209
12.3.2Locallinearfits209
12.4Globalnonlinearmodels211
12.4.1Polynomials211
12.4.2Radialbasisfunctions212
12.4.3Neuralnetworks213
12.4.4Whattodoinpractice214
12.5Improvedcostfunctions215
12.5.1Overfittingandmodelcosts216
12.5.2Theerrors-in-variablesproblem217
12.6Modelverification219
Chapter13Chaoscontrol223
13.1Unstableperiodicorbitsandtheirinvariantmanifolds224
13.1.1Locatingperiodicorbits225
13.1.2Stable/unstablemanifoldsfromdata229
13.2OGY-controlandderivates231
13.3VariantsofOGY-control234
13.4Delayedfeedback235
13.5Chaossuppressionwithoutfeedback235
13.6Tracking236
13.7Relatedaspects237
Chapter14Otherselectedtopics239
14.1Highdimensionalchaos239
14.1.1Analysisofhigherdimensionalsignals241
14.1.2Spatiallyextendedsystems245
14.2Analysisofspatiotemporalpatterns247
14.3Multiscaleorself-similarsignals,wavelets249
14.3.1Dynamicaloriginofmultiscalesignals250
14.3.2Scalinglaws252
14.3.3Waveletanalysis254
AppendixAEfficientneighboursearching257
AppendixBProgramlistings262
AppendixCDescriptionoftheexperimentaldatasets278
References288
Index300