《非线性时间序列分析（影印版）》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 real world is the analysis of time series from real systems in terms of nonlinear dynamics. This book provides experimentalists with methods for processing, enhancing, and analysing measured signals using these methods; and for theorists it demonstrates the practical applicability of ma

PrefaceViiAcknowledgementsiXPart1BasictopicsIChapter1Introduction:Whynonlinearmethods?3Chapter2Lineartoolsandgeneralconsiderations132.1Stationarityandsampling132.2Testingforstationarity152.3Linearcorrelationsandthepowerspectrum182.3.1Stationarityandthelow-frequencycomponentinthepowerspectrum222.4Linearfilters232.5Linearpredictions25Chapter3Phasespacemethods293.1Determinism:Uniquenessinphasespace293.2Delayreconstruction333.3Findingagoodembedding343.4Visualinspectionofdata373.5Poincaresurfaceofsection37Chapter4Determinismandpredictability424.1Sourcesofpredictability434.2Simplenonlinearpredictionalgorithm444.3Verificationofsuccessfulprediction464.4Probingstationaritywithnonlinearpredictions494.5Simplenonlinearnoisereduction51Chapter5Instability:Lyapunovexponents585.1Sensitivedependenceoninitialconditions585.2Exponentialdivergence595.3Measuringthemaximalexponentfromdata62Chapter6Self-similarity:Dimensions696.1Attractorgeometryandfractals696.2Correlationdimension706.3Correlationsumfromatimeseries726.4Interpretationandpitfalls756.5Temporalcorrelations,nonstationarity,andspacetimeseparationplots816.6Practicalconsiderations846.7Ausefulapplication:Determinationofthenoiselevel86Chapter7Usingnonlinearmethodswhendeterminismisweak917.1Testingfornonlinearitywithsurrogatedata937.1.1Thenullhypothesis957.1.2Howtomakesurrogatedatasets967.1.3Whichstatisticstouse997.1.4Whatcangowrong1027.1.5Whatwehavelearned1037.2Nonlinearstatisticsforsystemdiscrimination1047.3Extractingqualitativeinformationfromatimeseries108Chapter8Selectednonlinearphenomena1128.1Coexistenceofattractors1128.2Transients1138.3Intermittency1148.4Structuralstability1188.5Bifurcations1198.6Quasi-periodicity121Part2Advancedtopics123Chapter9Advancedembeddingmethods1259.1Embeddingtheorems1259.1.1Whitney'sembeddingtheorem1269.1.2Takens'sdelayembeddingtheorem1279.2Thetimelag1309.3Filtereddelayembeddings1349.3.1Derivativecoordinates1349.3.2Principalcomponentanalysis1359.4Fluctuatingtimeintervals1399.5Multichannelmeasurements1419.5.1Equivalentvariablesatdifferentpositions1419.5.2Variableswithdifferentphysicalmeanings1429.5.3Distributedsystems1439.6Embeddingofinterspikeintervals145Chapter10Chaoticdataandnoise15010.1Measurementnoiseanddynamicalnoise15010.2Effectsofnoise15110.3Nonlinearnoisereduction15410.3.1Noisereductionbygradientdescent15510.3.2Localprojectivenoisereduction15610.3.3Implementationoflocallyprojectivenoisereduction15910.3.4Howmuchnoiseistakenout?16310.3.5Consistencytests16710.4Anapplication:FoetalECGextraction168Chapter11Moreaboutinvariantqnantities17211.1Ergodicityandstrangeattractors17311.2LyapunovexponentsII17411.2.1ThespectrumofLyapunovexponentsandinvariantmanifolds17411.2.2Flowsversusmaps17611.2.3Tangentspacemethod17711.2.4Spuriousexponents17811.2.**lmosttwo-dimensionalflows18411.3DimensionsII18411.3.1Generaliseddimensions,multifractals18611.3.2Informationdimensionfromatimeseries18811.4Entropies18911.4.1Chaosandtheflowofinformation18911.4.2Entropiesofastaticdistribution19111.4.3TheKolmogorov-Sinaientropy19311.4.4Entropiesfromtimeseriesdata19411.5Howthingsarerelated19811.5.1Pesin'sidentity19811.5.2Kaplan-Yorkeconjecture199Chapter12Modellingandforecasting20212.1Stochasticmodels20412.1.1Linearfilters20412.1.2Nonlinearfilters20612.1.3Markermodels20712.2Deterministicdynamics20712.3Localmethodsinphasespace20812.3.1Almostmodelfreemethods20912.3.2Locallinearfits20912.4Globalnonlinearmodels21112.4.1Polynomials21112.4.2Radialbasisfunctions21212.4.3Neuralnetworks21312.4.4Whattodoinpractice21412.5Improvedcostfunctions21512.5.1Overfittingandmodelcosts21612.5.2Theerrors-in-variablesproblem21712.6Modelverification219Chapter13Chaoscontrol22313.1Unstableperiodicorbitsandtheirinvariantmanifolds22413.1.1Locatingperiodicorbits22513.1.2Stable/unstablemanifoldsfromdata22913.2OGY-controlandderivates23113.3VariantsofOGY-control23413.4Delayedfeedback23513.5Chaossuppressionwithoutfeedback23513.6Tracking23613.7Relatedaspects237Chapter14Otherselectedtopics23914.1Highdimensionalchaos23914.1.1Analysisofhigherdimensionalsignals24114.1.2Spatiallyextendedsystems24514.2Analysisofspatiotemporalpatterns24714.3Multiscaleorself-similarsignals,wavelets24914.3.1Dynamicaloriginofmultiscalesignals25014.3.2Scalinglaws25214.3.3Waveletanalysis254AppendixAEfficientneighboursearching257AppendixBProgramlistings262AppendixCDescriptionoftheexperimentaldatasets278References288Index300

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 real world is the analysis of time series from real systems in terms of nonlinear dynamics. This book provides experimentalists with methods for processing, enhancing, and analysing measured signals using these methods; and for theorists it demonstrates the practical applicability of mathematical results. The framework of deterministic chaos constitutes a new approach to the analysis of irregular time series. Traditionally, nonperiodic signals have been modelled by linear stochastic processes. But even very simple chaotic dynamical systems can exhibit strongly irregular time evolution without random inputs. Chaos theory offers completely new concepts and algorithms for time series analysis which can lead to a thorough understanding of the signals. The book introduces a broad choice of such concepts and methods, including phase space embeddings, nonlinear prediction and noise reduction, Lyapunov exponents, dimensions and entropies, as well as statistical tests for nonlinearity. Related topics such as chaos control, wavelet analysis, and pattern dynamics are also discussed. Applications range from high-quality, strictly deterministic laboratory data to short, noisy sequences which typically occur in medicine, biology, geophysics, and the social sciences. All the material discussed is illustrated using real experimental data. This book will be of value to any graduate student and researcher who needs to be able to analyse time series data, especially in the fields of physics, chemistry, biology, geophysics, medicine, economics, and the social sciences.