User:SxE00/IGEM 2006

Overview of my Contribution to IGEM

Advisor on Dynamic Systems

Here is an example of Bifurcation Diagram which we obtained during our various analyses.

Tutorials

The following tutorials were prepared to support the work of the Imperial College students participating in IGEM 2006.

• Analysis of a Dynamic System
  • Tutorial 1 : Basic Principles of Dynamic Analysis Dynamic Analysis
  • Tutorial 2 : Application of Poincare - bendixson Poincare Bendixson
  • Tutorial 3 : Template for the Analysis of a Dynamic System Template for Analysis
  • Tutorial 4 : Suggestions for the Presentation of Simulation Results Presentation

• Complementary Tutorials
  • Tutorial 5 : Curve Fitting with the Least Square Method Least Square Methods
  • Tutorial 6 : Solving a Cubic Equation (Cardano's Forumlae) Cardano

Analyses of Dynamic Systems

The final model was complex and depended on 8 independent parameters - 5 after rendering it dimension-less. In order to support the students in their analysis of the dynamic system ( and especially spare them the complex calculations) the following documents were prepared. Cases E=0 and E>0 were separated for practical and theoretical reasons:

- the case E=0 is a little bit simpler to study (one less parameter)

- but its study gives good insights into working out the calculations for the general case

- E=0 and E>0 exhibit some different characteristics as time goes to infinity

• Final Model with E=0
  • Part 1 : Obtaining the dimension-less form of the system Introduction (pdf)
  • Part 2 : A few remarks on the system A Few Remarks (pdf)
  • Part 3 : Finding the steady points of the system Steady Points (pdf)
  • Part 4 : Are trajectories bounded? (available soon in pdf)
  • Part 5 : Stability Analysis Stability Analysis (pdf)

• Final Model with E>0
  • Part 1 : Obtaining the dimension-less form of the system Introduction (pdf)
  • Part 2 : A few remarks on the system A Few Remarks (pdf)
  • Part 3 : Finding the steady points of the system Steady Points (pdf)
  • Part 4 : Are trajectories bounded? Behaviour at Infinity (pdf)
  • Part 5 : Stability Analysis Stability Analysis (pdf)
  • Part 6 : Conclusion - how to get an oscillator Oscillations (pdf)