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Physics
Applied and Interdisciplinary Physics
Nonlinear Dynamics and Chaos
1. Introduction to Dynamical Systems
2. One-Dimensional Flows
3. Two-Dimensional Flows
4. Higher-Dimensional Systems
5. Introduction to Chaos in Continuous Systems
6. Discrete Dynamical Systems and Maps
7. Universality and Scaling
8. Fractal Geometry
9. Hamiltonian Dynamics and Conservative Systems
10. Synchronization Phenomena
11. Control of Chaos
12. Spatiotemporal Dynamics
13. Time Series Analysis
14. Applications in Physical Sciences
15. Applications in Life Sciences
16. Applications in Chemistry
17. Applications in Engineering
18. Applications in Economics and Social Sciences
19. Computational Methods
13.
Time Series Analysis
13.1.
State Space Reconstruction
13.1.1.
Takens' Embedding Theorem
13.1.2.
Method of Delays
13.1.3.
Choosing Embedding Parameters
13.1.3.1.
Time Delay Selection
13.1.3.2.
Embedding Dimension
13.1.4.
False Nearest Neighbors
13.2.
Nonlinear Time Series Analysis
13.2.1.
Recurrence Plots
13.2.2.
Recurrence Quantification Analysis
13.2.3.
Correlation Dimension Estimation
13.2.4.
Lyapunov Exponent Calculation
13.3.
Distinguishing Chaos from Noise
13.3.1.
Surrogate Data Methods
13.3.2.
Nonlinear Prediction
13.3.3.
Noise Reduction Techniques
13.4.
Applications to Real Data
13.4.1.
Preprocessing Techniques
13.4.2.
Stationarity Testing
13.4.3.
Nonlinearity Tests
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14. Applications in Physical Sciences