1. Three resulting equations describing the Overall System:
Modelling:
Full System Model
Three resulting equations describing the Overall System:
Production of AHL
Degradation of AHL by enzyme
“Natural” degradation of AHL

2. Can we have oscillations?
Simplified 2-D model
Assume δaiiA = δ2LuxR and [aiiA]initial = [LuxR]initial
Can we have oscillations?
[aiiA] = [LuxR]!!!

3. Final model is too complicated to analysis at the beginning
Pure Lotka-Volterra
Final model is too complicated to analysis at the beginning
We need a basic understanding on Lotka-Volterra model
We first analyse the original LV model because it is simpler
Dynamic Analysis
1. Finding Stationary points
Two stationary points (0,0), (d/c, a/b)
2. Analysing the stability of points
Jacobian Analysis
(0,0) is always an unstable point
(d/c, a/b) is always a center

4. How about our system? Complicated model
Zone 3:
3 stationary Points
Zone 2:
2 stationary Points E R
E=1
Zone 1:
1 stationary Point
E=R/(R+1)
E=R2/(R+1)2
R=1
Zone 4:
3-5 stationary Points
How about our system?
Normalised to dimensionless form
Zone 3:
3 stationary Points

5. Complicated model
What we could improve the parameter, and the expected result
Results generated by real parameter from experiments