Lecture 26

Lectures: 1 | 2 | 3 | 4-5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 15 | 16 | 17 | 19 | 20 | 21 | 22 | 23 | 26

Dynamic Behaviors

Stability of Fixed Points:
- Linear Stability Matrix; Eigenvectors and Eigenvalues (Routh-Hurwitz Theorem)
- Loss of Stability from a Real Eigenvalue; Stability Exchange, Bifurcation (Page 1 (GIF))
- Loss of Stability from Imaginary Eigenvalues; Poincare Cycles
- Simple (Harmonic) Oscillator, and Complex Representation (Page 2 (GIF))
Biochemical Clocks:
- The Belousov-Zhabotinsky Reaction
- The Cogs of a Biological Clock
- Animations of Biological Clocks
- The Repressilator (PDF) [Elowitz and Liebler. Nature 403, no. 305 (2000)]
Synchronization:
- Examples: Heart Pacemaker Cells, Fireflies, Cycada.
- The Kuramoto Model (Java® Applet by Albert Diaz-Guilera)
- Collective Synchronization (Page 3 (GIF) and Page 4 (GIF) of Lecture Notes)
Biological Patterns:
- Morphogenesis is the Process Whereby a Living Organism Develops Form and Structure, e.g.
  - Animal Coats and Pigmentation Patterns
- Where do Spots Come From? Turing's Answer
  - Reaction-Diffusion Equations (Page 5 (GIF) of Lecture Notes)
  - Constraints for a Finite Wave-length Instability (Page 6 (GIF) of Lecture Notes)
  - Long-range Inhibition and Short-range Excitation (Page 7 (GIF) of Lecture Notes)