Time  8:00 to 8:50 AM MWF  
Place  CAVS classroom  
Instructor 
Joseph Picone Office: 2133 CAVS Office Hours: by appt. Email: picone@ece.msstate.edu 

URL  http://www.cavs.msstate.edu/research/isip/publications/courses/ece_7000_nonlinear  
Required Textbook(s)  Kantz and Schreiber Nonlinear Time Series Analysis, Cambridge, ISBN: 0521529026, 2004.  
Prerequisite  Familiarity with Linear Systems, Linear Signal Modeling techniques (e.g., Linear Prediction, Spectral analysis)  
Reference Textbook(s) 
Henry D.I. Abarbanel,
Analysis of Observed Chaotic Data,
Springer, ISBN: 0387983724, 1997.
G.L. Baker and J.P. Gollub Chaotic Dynamics  an introduction, Cambridge, ISBN: 0521382580, 1990. David Ruelle Chance and Chaos, Princeton University Press, ISBN: 0691085749, 1991. S.J. Orfandis, Introduction to Signal Processing, PrenticeHall, ISBN: 0132091720, 1996. 
Final report  50% 
Special assignments  25% 
Lecture preparation  25% 
Class  Date  Section(s)  Scribe  Topic(s) 
01  01/20  Introduction  SP,SR  Introduction to Linear Signal Analysis techniques 
02  01/20  Introduction  SP,SR  Dynamics of a system in the Phase Space 
03  01/25  2  SL  Review of Linear techniques1 
04  01/27  2  DM  Review of Linear techniques2 
05  01/30  2  MP  Phase Space Methods 
06  02/01  3  SP  Reconstructed Phase Spaces 
07  02/03  4  SR  Determinism and Predictability 
08  02/06  4  4.3  JS  Determinism and Predictability 
09  02/08  4  SL  Nonlinear Time Series Prediction 
10  02/10  5  DM  Lyapunov Exponents 
11  02/13    Review  Review of lectures 1 through 6 
12  02/15  6  MP  Correlation Integral and Dimensions 
13  02/17  6  SP  Correlation Dimension Estimation 
13  02/17  6  SR  Multiscale and Self Similar Signals 
15  02/22  6  JS  Multiscale and Self Similar Signals 
16  02/24  7  SL  Testing Nonlinearity with Surrogate Data 
17  02/27  7  DM  Testing Nonlinearity with Surrogate Data 
18  03/01  8  MP  Selected Nonlinear Phenomena  Bifurcation and Intermittency 
19  03/03  8  SP  Selected Nonlinear Phenomena  Quasiperiodicity 
20  03/06  9  SR  Advanced Embedding Methods 
21  03/08  9  JS  Advanced Embedding Methods 
22  03/20  9  SL  Advanced Embedding Methods 
23  03/22  9.49.6  DM  Fluctuating Time intervals 
25  03/24  4.4.3, 8.3  MP  TBD 
26  03/27  8.4  SP  SVD Embedding 
27  03/29  10  SR  Local Projective noise Reduction 
28  03/31  10  JS  Local Projective noise Reduction 
30  04/03  11.1  SL  Ergodicity and strange attractors 
31  04/05  TBD  DM  Estimating Correlation integral from a time series 
32  04/07  TBD  MP  Correlation Dimension 
33  04/10  TBD  SP  TBD 
34  04/12  TBD  SR  TBD 
35  04/17  12.212.4  JS  TBD 
36  04/19  12.512.7.3  SL  Overfitting and model Verification 
37  04/21  TBD  DM  TBD 
38  04/24  TBD  MP  TBD 
39  04/26  TBD  SP  TBD 
40  04/28  TBD  SR  TBD 
41  05/01    JS  Review of chapter 8 
42  05/03    Review  Review of lectures and discuss term paper 
43  05/05  Cumulative  TBD  Final report 