מערכות דינמיות סמ 1

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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 slides	Strogatz, "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 exercises	Strogatz, "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 exercises	Strogatz, "Nonlinear Dynamics and Chaos", Sections 3.5,3.7
  4	Linear and nonlinear 2D systems: fixed points and manifolds Slides: PPT and  PDF Home exercises	Strogatz, "Nonlinear Dynamics and Chaos", Chapter 5 and Sections 6.0-6.4
  5	Conservative systems and limit cycles Slides: PPT and  PDF Home exercises	Strogatz, "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 exercises	Strogatz, "Nonlinear Dynamics and Chaos", Sections 7.2-7.6
  7	Generalization of bifurcations in 2D and center manifold reduction Slides: PPT and  PDF Home exercises	Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.0-8.3 Review paper: Crawford, Introduction to bifurcation theory, Rev. Mod. Phys., 1991
  8	Stability (Floquet theory) and global bifurcations of cycles Slides: PPT and PDF Home exercises	Strogatz, "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., 2008
  15/16/23.12	Mid-term project presentations by students Questions/Answers meeting Presentations 15/12, Presentations 16/12, Presentations 23/12	Mid-term project guidlines
  9	Lorentz equations and chaos Slides: PPT and PDF Home exercises	Strogatz, "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 Chaos
  10	One dimensional maps (Poincaré sections), period-doubling, and route to chaos  Slides: PPT and PDF Home exercises	Strogatz, "Nonlinear Dynamics and Chaos", Sections 10.0-10.6
  11	Aperiodic dynamics, frequency locking, and Fractals Slides: PPT and PDF Home exercises	Strogatz, "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

  
  

  • Final project: submission in PDF format Assignment
  
• 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

  • S.H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering, 2^nd Edition, CRC Press 2015

  
  

  Additional literature

  • D. Kaplan and L. Glass, Understanding Nonlinear Dynamics, Springer Science+Business Media New York, 1995

  • J.D. Murray, Mathematical Biology (Parts I & II), 3^rd 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.