Topics in Nonlinear Time Series Analysis: With Implications for EEG AnalysisWorld Scientific, 2000 - 342 Seiten This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented ? algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram. |
Inhalt
Introduction | 1 |
Dynamical systems time series and attractors | 9 |
Linear methods | 39 |
Theoretical founda | 49 |
Practical application | 73 |
Basic definitions | 93 |
Lyapunov exponents and entropies | 113 |
Numerical estimation of the correlation dimen | 123 |
8 | 173 |
Monte Carlo analysis of dimension estimation | 183 |
ding parameters | 216 |
Surrogate data tests | 221 |
Dimension analysis of the human EEG | 249 |
Testing for determinism in time series | 273 |
Conclusion | 309 |
337 | |
Andere Ausgaben - Alle anzeigen
Topics in Nonlinear Time Series Analysis: With Implications for EEG Analysis Andreas Galka Eingeschränkte Leseprobe - 2000 |
Häufige Begriffe und Wortgruppen
algorithm amplitude application of GPA apply approach approximately autocorrelation average behaviour chapter chosen convergence coordinates Correlation dimension estimate correlation integral correlation sum corresponding curves d₂ delay denote derivative deterministic dimension analysis dimension estimate versus distances distribution dynamical system EEG time series embedding dimension employ entropy equation estimate versus radius Euclidean metric evaluate filter fractal dimension frequency function gaussian generalised dimensions given Grassberger Hausdorff dimension hypercube information dimension ISI series left panel linear local-slopes Lorenz attractor Lyapunov exponents Mackey-Glass system maximum metric multiple Lorenz systems N,-spheres Ndist nonlinear time series nonstationary null hypothesis obtain onefold Lorenz original time series oscillation pointwise dimensions power spectrum right panel sampling scaling region series analysis shown in figure slope space reconstruction standard deviations statistical error stochastic strange attractors surrogate data testing Theiler correction theorem time-delay reconstruction trajectory true state space twofold Lorenz values vectors white noise zero
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