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
The EP structure of the lac operon model
Summary --- The EP structure of the lac operon model.
- how to find EPs in the lac op model: algebra vs geometry
- graphical method -> 3 EPs
- determining stability of the 3 EPs
- a biological “switch” in the lac operon
- features of a biological switch:
- low EP ≠ 0 (always some on hand)
- low EP stable -> no runaway excitation
- there is a “threshold” (= unstable EP), after which there is a new mode that is a high EP which is stable.
