1
State Space
2
Operating with Vectors
3
Trajectories and Time Series
4
Models and Change Vectors
- 4.1 Introduction to Models and Change Equations: The Bathtub4.2 Models and Change Equations in 2 Dimensions: Shark Meets Tuna4.3 From Change Equations to Change Vectors4.4 State spaces and change vectors in 2D4.5 Trajectories in 2D4.6 Logistic Growth4.7 Models and Vectorfields: a nonlinear example in 1D4.8 Modeling Chemical Reactions4.9 Epidemiology4.10 Immune Dynamics
5
Euler's Method
7
Linear Stability Analysis
8
Higher Dimensions
9
The Lac operon: a biological switch
10
Bifurcation
12
The Central Dogma
13
Stable Oscillations in Science (and Music)
14
Oscillations in Physiology
16
Chaos 1
17
Chaos 2
19
Chaos 4
20
Chaos and Cardiology
21
Applications of Linear Algebra
Ventricular Fibrillation
Summary --- Ventricular Fibrillation
- even though VF is a complex phenomenon, it is chaotic and not random.
- Because it is chaotic, there are parameters that can be lowered to take the system out of its chaotic behavior.
- We found a critical parameter, the slope of the cell’s recovery function from the previous stimulus. When this slope was reduced by a drug, the fibrillation reverted to a simpler non-chaotic behavior.
- This was seen first in computer simulation, and subsequently in animal experiments.