Lecture 4

Dimensional analysis, competitive networks, phase plane analysis

Dimensional analysis
Dynamics of on–center off–surround shunting competitive networks
Phase plane analysis of competitive networks

Dimensional analysis

• http://en.wikipedia.org/wiki/Dimensional_analysis
• Lin, C.C., & Segel, L.A. (1974) Mathematics Applied to Deterministic Problems in the Natural Sciences. New York: Macmillan.
  • Chapter 6: Simplification, dimensional analysis, and scaling , pp. 185–224
• Edelstein–Keshet, Leah (1988) Mathematical Models in Biology. SIAM Classics in Applied Mathematics, vol. 46.
  • Section 4.3: Formulating a model
  • Section 4.4: Saturating nutrient consumption rate
  • Section 4.5: Dimensional analysis of the equations

Phase plane analysis

• http://en.wikipedia.org/wiki/Phase_plane
• Edelstein–Keshet, Leah (1988) Mathematical Models in Biology. New York: Random House.
  • Sections 5.2–5.9: Phase–plane methods and qualitative solutions , pp. 171–193.
• Blanchard, Paul, Devaney, Robert L., and Hall, Glen R. (2002) Differential Equations. Second Edition. Pacific Grove, CA: Brooks/Cole. [+ solutions]
  • Boston University Ordinary Differential Equations Project: http://math.bu.edu/odes/
  • Section 3.3: Phase planes for linear systems with real eigenvalues, pp. 266-282.
  • Section 5.2: Qualitative analysis, pp. 457-470.
  • Section 5.3: Hamiltonian systems, pp. 470-488. http://en.wikipedia.org/wiki/Hamiltonian_mechanics
  • Section 5.4: Dissipative systems, pp. 488-510. http://en.wikipedia.org/wiki/Dissipative