TVI: Nonlinear Dynamics and Complex Systems (Prof. Erwin Frey)

Monday and Thursday, 10:15 - 12:00
Arnold Sommerfeld room 349, Theresienstr. 37, 3rd floor

• Nonlinear Dynamics - Motivation (15. oct. 2007) [pdf]
• 1. Introduction (18. oct. 2007) [pdf]
• 2. 1-dim. systems (22. oct. 2007) [pdf]
  • 2.3. Bistable potentials (25. oct. 2007) [pdf]
  • 2.5.4. An insect outbreak model (29. oct. 2007) [next pdf]
• 3. 2-dim. flows (29. oct. 2007) [pdf]
  • 3.2. Nonlinear Systems (08. nov. 2007) [next pdf]
  • 3.3. Interacting Populations (08. nov. 2007) [pdf]
    • 3.3.2. Competitive Models (12. nov .2007) [next pdf]
  • 3.4. Limit Cycles & Nonlinear Oscillators (12. nov .2007) [pdf]
    • 3.4.3. Glycolysis (15. nov. 2007) [next pdf]
    • 3.4.5. Weakly nonlinear oscillators (15. nov. 2007) [pdf]
• 4. Propagating signals in excitable media (19. nov. 2007) [pdf]
  • (4.1.3.) (22. nov. 2007) [next pdf]
  • 4.2. Oscillatory and Excitable Media (22. nov. 2007) [pdf]
    • (4.2.2.) (26. Nov. 2007) [next pdf]
  • 4.2.3. Spiral Waves (26. Nov. 2007) [pdf]
  • (4.2.3.) (29. nov. 2007) [next pdf]
• 5. Local Bifurcation Theory (29. nov. 2007) [pdf]
  • (5.1.) (03. dec. 2007) [next pdf]
  • 5.2. Normal Forms (03. dec. 2007) [pdf]
  • (5.2.) (10. dec. 2007) [pdf]
  • 5.3. Bifurcation of Fixed Points (17. dec. 2007) [pdf]
• 6. Linear Stability Analysis of Pattern-Forming Systems (21. dec. 2007) [pdf]
  • 6.2. Reaction-Diffution Systems and the Turing-Instability (07. jan. 2008) [pdf]
  • 6.3. General Frame Work of a Linear Stability Analysis (10. jan. 2008) [next pdf]
• 7. Nonlinear States and Amplitude Equations (14. jan. 2008) [pdf]
  • 7.3. Amplitude Equation for Stripe States (17. jan. 2008) [pdf]
  • 7.4. Amplitude Equation for Stripes in Uniaxial Systems (10. jan. 2008) [pdf]
  • 7.6. Amplitude Equation for Oscillatory Media (21. jan. 2008) [pdf]
• 8. Instabilities of Stripes and Traveling Plane Waves (24. jan. 2008) [pdf]
• 9.Spirals and Defects (28. jan. 2008) [pdf]
• (remaining records) (14. jan. 2008) [pdf]

• appendix A: Langmuir Kinetics [pdf]

supplementary material

• Continuous Population Models () [pdf]
• Differential Equations (5. nov. 2007) [pdf]
• Space Curves (27. nov. 2007) [pdf]
• Singular perturbation theory of traveling waves in excitable media (29. nov. 2007) [pdf]
• Variationsrechnung [pdf]
• Evolutionary Game Theory (6.Dez.2007) [pdf]
• Webpage of Michael Cross [link]

• F.J. Isaacs et al., Prediction and measurement of an autoregulatory genetic module,
  PNAS 100, 7714-7719 (2003).
• C. Hauert et al., Evolutionary games and population dynamics: maintenance of cooperation in public goods games,
  Proc. R. Soc. B (2006) 273, 2565.
• Süel et al., An excitable gene regulatory circuit induces transient cellular differentiation,
  Nature 440(7083), 545-550 (2006).
• Alain Karma and Robert F. Gilmour Jr, Nonlinear dynamics of heart rhythm disorders,
  Physics Today 60(3), 51-57.
• Kevin Hall et al., Dynamic Control of Cardiac Alternans,
  Phys. Rev. Lett. 78, 4518 - 4521 (1997).
• James P. Keener, Symmetric spirals in media with relaxation kinetics and two diffusing species,
  Physica D: Nonlinear Phenomena, Volume 70(1-2), 61-73 (1994).

• How to get access to articles [page of LRZ]

Links

• A: Biophysik der Systeme

Physical

• Hydrodynamik und Strukturbildung (with short introduction to continuum mechanics) [link]

Biological

• H. Meinhardt, The Algorithmic Beauty of Sea Shells, Springer Verlag

Mathematical (Introductory)

• S.H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press (einführend)
• P. Glendinning, "Stability, Instability and Chaos", Cambridge University Press.
• D.W. Jordan and P. Smith, "Nonlinear Ordinary Differential Equations", Oxfor University Press

Mathematical (Advanced)

• S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer Verlag
• J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vetor Fields", Springer Verlag

• XPPAUT website.
• Installation:
  • Linux users: If XPPAUT is not included in your linux distribution, download this source file, extract it into a directory, and install it as usual by "make".
  • Windows users: Follow this short guide.
• .ode files of the excercise: [zip]
• Further documentation: There is a detailed online tutorial, where you can lern more than the basics given in the exercise.