MCE 567 – Experimental Nonlinear DynamicsCourse Information & SyllabusSpring 2011 Semester. Professor Dr. David Chelidze office: 128C KirkProfessor phone: 874.2356Mechanical Engineering email: [email protected] & Time Wales Hall 223 on Tuesdays and Thursdays from 11:00 a.m. – 12:15 p.m.Office Hours Tuesdays and Thursdays 9:30–10:30 a.m. or by appointment. To make anappointment, please see me at class time or contact me via email.Web Site http://www.mce.uri.edu/chelidze/courses/mce567/Required Texts Holger Kantz and Thomas Schreiber, Nonlinear Time Series Analysis, SecondEdition, Cambridge, 2004.Optional Texts Chaos and Time-Series Analysis, J. C. Sprott, Oxford Univ. Press, 2003.Lawrence N. Virgin, Introduction to Experimental Nonlinear Dynamics: ACase Study in Mechanical Vibration, Cambridge University Press, Cambridge,United Kingdom, 2000.J. M. Cushing, et al., Chaos in Ecology: Experimental Nonlinear Dynamics,Academic Press, Elsevier Science, 2003.Course Work There will be no formal exams. However, I plan on conducting several in-classquizzes. The class will run as an advance seminar, and class participationand discussion is expected and strongly encouraged. There will be five toseven substantial assignments given to you during this course. These as-signments will include problems requiring a straightforward application ofmethods covered in class or described in books as well as open-ended prob-lems that might not have definite “answers.” The final assignment can bereplaced with a project tailored to the individual student’s research interest.Use of computers while working on your assignments is strongly encouraged.It is important to be able to find numerical solutions and do tedious alge-braic manipulations using MATLAB, Mathematica, Mathcad, etc. MATLABand Mathematica are available on variety of platforms in ECC and ChamplinComputer Classroom.General You are encouraged to collaborate on the assignments, in the form of dis-cussing difficulties, ideas, etc. with other students. However, copying isstrictly prohibited and will be viewed as a serious violation of ethics. If youcannot differentiate between the two, please ask for clarification. All workmust be neat and easy to read or it will be returned to you. Write only onone side of a page, and do not turn in all of your scratch work.GradingCategory Percent of GradeQuizzes 20%Assignments 50%Final Project 30%Brief Course OutlineWe will cover as much of this outline of topics as we can.1. Introduction – Statistical and Spectral Analysis of Linear Systems• Probability, estimators, stationarity and sampling from dynamical systems perspec-tive; Linear (auto)correlation, Fourier and power spectrum; and Linear filters andmodels.2. Bifurcation and Poincar´e maps• Phase space and the Poincar´e section; Bifurcations; and Stability of equilibria andmotion.3. Delay Reconstruction and Embedding• Embedology; Dimension theory; Invariant measures of an attractor; and Empiricaldata-based models.4. Experimental Systems• Experimental dimension estimates; and Stability and Lyapunov exponents.5. Advanced Topics• Advanced embedding methods; Chaotic data and noise; Nonlinear modeling andforecasting; Nonlinear normal modes; Nonstationary systems; and Chaos synchro-nization and