Physics 648 - Nonlinear Dynamics - Spring 2022

Instructor Renate Wackerbauer,
Office Location: REIC 106
phone: 474-6108                                 WELCOME !! and have a great semester
Open office hours Due to Covid19 there are no walk-in office hours unless the situation improves; discussions after class work well; meeting via zoom works; email is effective for straight-forward questions. additional recitation classes can be scheduled on request.
Course info Phys648, 3 credits
Prerequisites graduate standing or instructor's permission
Lectures MWF 13:00 to 14:00 pm, REIC 202.
Lectures are face to face
Due to the fluid situation with covid, the course modality can change throughout the semester. In the case of online course delivery, lectures would be offered synchronously (tablet with whiteboard), recorded, and uploaded into google classroom.
Noyes Lab Access to the Noyes Computer Lab (Rm 101 REIC is provided to all students enrolled in a Physics course. Your polar express card lets you in.

Required text: 
Nonlinear Dynamics and Chaos, by S. Strogatz, Perseus Publishing.
(book is available as hard copy and as electronic copy at Rasmuson library)

Supplementary readings:
Chaotic dynamics,  by T. Tel and M. Gruiz, Cambridge (2007).
  many nice applications, and great explanations.
Chaos in dynamical systems,  by E. Ott, Cambridge (2002).
   also covers Hamiltonian chaos and quantum chaos.
Applied nonlinear dynamics, by A. Nayfeh, B. Balachandran, Wiley (2004).
   covers analytical, computational and experimental methods in one book!!
An exploration of Chaos, 
by Argyris, Faust, and Haase, Elsevier (1994). 
   nice examples, some detailed calculations that are helpful for understanding
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, by Guckenheimer and Holmes, Springer (1983).
   THE standard book in nonlinear dynamics from an applied mathematical sciences point of view
Synchronization, a universal concept in nonlinear science, by Pikovsky, Rosenblum and Kurths, Cambridge (2001).
   a particular focus on synchronization, with many many examples across disciplines
Nonlinear time series analysis, by Kantz and Schreiber, Cambridge (1998)
   focuses on NLD and its applications to the analysis of time series, discusses pitfalls, shows many applications
Mathematical Biology I and II, by J.D. Murray, Springer (3rd edition, 2002) 
   on nonlinear dynamics with particular focus on biological systems
Mathematical Geoscience, by Andrew Fowler, Springer (2011)

There are many books on nonlinear dynamics in the library. Please explore them to see different approaches to our topics.

Course Content

Tentative course calendar

Introduction into the dynamics of nonlinear systems. Continuous and discrete dynamical systems, stability analysis, bifurcations, limit cycle, chaos and strange attractors, fractals and dimension algorithms, controlling chaos, synchronization processes, and stochastic dynamical systems.

Course Goals, Student Learning Outcomes

This course provides an introduction into nonlinear dynamics at the graduate level. Dynamical systems that are characterized with coupling and feedback processes often show dynamical or spatiotemporal patterns that need to be described at the systems level; a reductionist approach is not suited for complex systems, since the entire system behaves different to the sum of its part. Complex systems can be high-dimensional but must not. A necessary requirement for complex dynamics is nonlinear equations of motion.

Students learn,
*how to analyze the stability of complex systems
*how nonlinear systems differ from linear systems regarding dynamical properties
*how sensitivity of system dynamics is related to predictability, determinism, and control
*to explore dynamical systems analytically and with computer simulations


homework assignments

Homework will be assigned weekly and will be due by 3:00 pm on the following Friday, unless explicitely altered at the time of assignment. Late homework will not be accepted. Finished homework should be uploaded to "google classroom" in a single pdf-file. Solutions will be posted in the glass case in the Physics Department hallway.
in case of issues with the homework link use:
Project: Paper & Presentation

Explore nonlinear dynamics with a project that includes a computational component! For example a bifurcation analysis of a dynamical system, the calculation of fractal dimensions of certain cracks; nonlinear time series analysis of an ECG, or other biological, financial, physical measurement series; correlations between two time series (synchronization); phase space analysis and quantification. Explore a topic related to this course on your own. The project needs to be based on a published paper or text book, online sources like Wikipedia are not allowed. A list of possible topics is given here: topics. You can also choose a topic of your interest in agreement with the instructor. All topics should be discussed with the instructor at least 5 days before the topic is due. 

Project on track: 1) project topics [20points]: submit tentative project title and a pdf file of the main literature source (paper, text book) that you use in your project. topics are due on Feb. 16. 2) project outline [30points]: submit a one page paper proposal that includes a) scientific background, b) hypothesis to test, and c) scientific approach and methods to be used. outline is due on March 2. 3) project simulation [50points]: submit one page that describes a) computational methods used, b) a first simulation result that demonstrates that you have a basic working computer program towards your project [this can be done through a figure and its description; figures don't count towards page requirements], and c) a brief outline of the remaining computational study to be done. project simulation is due march 16.

Project paper: The results of your project should be turned in as a paper, like an article in the journal "Physics Today". It should consist of 5 pages [11pt, standard margins (not larger than 1inch) and spacing, single column), including introduction, NLD background, results and discussion, summary, and about 5 references.  figures and references do not count towards the 5 pages. The paper needs  to be turned in as a PDF-file and as a HARD COPY. The grade is determined from physics (60%) and style (40%) of the paper. The physics part includes correct physics, level covered, computational results, how explained, how introduced, understanding, terms defined. The style part includes organization and structure, title, references given, figures referenced, good to read, grammar. the paper is due Wednesday, April 6.

Presentation: The paper will be presented to the class in a 15 minutes talk (excluding discussions) the week before finals; an electronic copy of the presentation needs to be turned in on the day of the presentation. The grade is determined from clarity of presentation (50%) and content (50%). The clarity of presentation includes board/transparency use, clarity of writing/slides, references used, blocking board/screen, speaking clearly and loud, speed of speach, facing class and eye contact, dealing with questions. The content includes appropriate level, enough details, terms introduced before used, correct physics, how explained.


A one-hour in-term examination and a two hour final examination will be held during the semester. In-term exams will be held in the classroom. The exams will be closed books and closed notes.

Midterm exam Friday, Feb 25
Strogatz, approx chapt 1-7
Final exam Wed, April 27, 1-3pm Strogatz, approx chapt 1-12
Grading The maximum score for each homework will be 100 points. A solution (homework, exam) that presents nothing more than a restatement of the problem will receive zero credit. Credit will be given for clarity of presentation, illegible work will not be graded. Grades are assigned as follows: A+ (>97.5%), A (>87.5%), A- (>85%), B+ (>82.5%), B (> 72.5%), B- (>70%), C+ (> 67.5%), C (> 57.5%), C- (> 55%), D+ (> 52.5%), D (> 42.5%), D- (> 40%), else F. For the final grade homework, exams, etc. will be weighted as follows:
Homework 25%
Presentation 15%
Paper 15%
Project on track
Midterm 20%
Final exam 20%
Course policies Attendance at lectures is expected. Active class participation, questions, comments on newspaper articles on modern physics are extremely welcome in the lectures. A missed exam will receive 0 credit unless the instructor is notified by email, phone, etc before the exam starts. Make-up exams will be individually scheduled with the student.
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