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Topics
Week Topic Additional reading 1 Formalities, motivation, and course overview
Slides: PPT and PDF
At home: watch the movie on slide 37 of the class slidesStrogatz, "Nonlinear Dynamics and Chaos", Chapter 1 and Sections 2.0-2.3 2 Linear stability in 1D, bifurcation theory, and numerical methods for ODEs
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 3.0-3.2, 3.4, 2.8 3 Qualitative analysis: effect of time scales and parameters
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 3.5,3.7 4 Linear and nonlinear 2D systems: fixed points and manifolds
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Chapter 5 and Sections 6.0-6.4 5 Conservative systems and limit cycles
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 6.5-6.7, 7.0-7.1 6 Closed orbits (Poincaré-Bendixson theorem) and nonlinear oscillations
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 7.2-7.6 7 Generalization of bifurcations in 2D and center manifold reduction
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Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 8.0-8.3
Review paper: Crawford, Introduction to bifurcation theory, Rev. Mod. Phys., 19918 Stability (Floquet theory) and global bifurcations of cycles
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 8.4-8.7
Easy paper stability of cycles: Klausmeier, Floquet theory: a useful tool for understanding nonequilibrium dynamics, Theor. Ecol., 200815/16/23.12 Mid-term project presentations by students
Questions/Answers meeting
Presentations 15/12, Presentations 16/12, Presentations 23/12Mid-term project guidlines 9 Lorentz equations and chaos
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 9.1-9.3, 12.0-12.1, 12.4
Short notes that include some of the topics: Nonlinear Dynamical Systems, Their Stability, and Chaos10 One dimensional maps (Poincaré sections), period-doubling, and route to chaos
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 10.0-10.6 11 Aperiodic dynamics, frequency locking, and Fractals
Slides: PPT and PDF
Home exercisesStrogatz, "Nonlinear Dynamics and Chaos", Sections 8.6, 10.7, 11.0-11.3, 12.0-12.3 12 Introduction to pattern formation (nonlinear PDEs)
Slides: PPT and PDF- Whitesides and Grzybowski, Self-assembly at all scales, Science 295, 2418 (2002) - short overview
- Cross and Hohenberg, Pattern formation outside of equilibrium, Reviews of Modern Physics 65, 851 (1993) - detailed review
20.3 Final project assignments guidelines
Lecture, Tutorial and office hours
Office hours
Name Day Hours Building/Room E-mail Dr. Arik Yochelis By appointment - 54/220 yochelis@bgu.ac.il
Lecture/Tutorial
Group What? Name Day Hours Building/Room 1 Lecture Dr. Arik Yochelis Tuesday 15:30-17:00 ZOOM 2 Lecture (optional by request) Dr. Arik Yochelis Wednesday 14:00-15:00 ZOOM Homework exercises
Textbooks
Main book
Additional literature
J.D. Murray, Mathematical Biology (Parts I & II), 3rd Edition, Springer, 2007
j.D. Crawford, Introduction to bifurcation theory, Rev. Mod.; Phys., 1991
Class exercises
Course policy
Grading
- Homework (0 points):
- Mid-term project, 40%
- Final project, 60%
General
- Email: should only be used for communication on personal matters, all questions of relevance to more than one person should be asked via the Q&A forum, to avoid repetition.