User:SxE00/IGEM 2006: Difference between revisions

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== Overview of my Contribution to IGEM ==
== Overview of my Contribution to IGEM ==


I have been an Advisor on Dynamic Systems for the IGEM Imperial College Team.
As an advisor I have supervised the study by Imperial IGEM students of ever more complex dynamic systems (from the simple Lotka-Volterra [link] to the complex 2D prey-predator model with bounded  growths and killings [link]).


Here is an example of Bifurcation Diagram which was obtained by the team during the various analyses.


Here is an example of Bifurcation Diagram which we obtained during our various analyses.
[[Image:Bifurcation Diagram.jpg]]
 
== Specific Contributions ==
 
*Teaching the Basics of Dynamic Systems
:*Generalities
::- What is a Dynamic System?
::- How do you interpret the parameters of a Dynamic System?
:::Focus on the Prey-Predator Models
::- What is a Steady Point? Why are so Important?
::- Why do we study the Jacobian to study Dynamic analysis?
:* Lecture on Dynamic Systems [[IGEM:IMPERIAL/2006/Calendar/2006-8-9]]


[[Image:Bifurcation Diagram.jpg]]
*Support for Students
:* Support in Mathematics
::- Help for Data Analysis (Methods/Implementation)
::- Help for Calculations in Study of Dynamic Systems
:* Creation of Tutorials for IGEM Students (see below) including
::- Templates for Study of Dynamic Systems
::- templates for Presentation of Results


== Tutorials ==
== Tutorials ==
Line 16: Line 36:
** Tutorial 3 : Template for the Analysis of a Dynamic System [http://www.openwetware.org/images/e/ea/WIKI_Document_Number_3_-_Template_for_Analysis.pdf  Template for Analysis]
** Tutorial 3 : Template for the Analysis of a Dynamic System [http://www.openwetware.org/images/e/ea/WIKI_Document_Number_3_-_Template_for_Analysis.pdf  Template for Analysis]
** Tutorial 4 : Suggestions for the Presentation of Simulation Results [http://www.openwetware.org/images/1/18/WIKI_Document_Number_4_-_Presentation_of_Results.pdf  Presentation]
** Tutorial 4 : Suggestions for the Presentation of Simulation Results [http://www.openwetware.org/images/1/18/WIKI_Document_Number_4_-_Presentation_of_Results.pdf  Presentation]


* '''Complementary Tutorials'''
* '''Complementary Tutorials'''
** Tutorial 5 : Curve Fitting with the Least Square Method [http://www.openwetware.org/images/5/5c/WIKI_Document_Number_5_-_Curve_Fitting.pdf  Least Square Methods]  
** Tutorial 5 : Curve Fitting with the Least Square Method [http://www.openwetware.org/images/5/5c/WIKI_Document_Number_5_-_Curve_Fitting.pdf  Least Square Methods]  
** Tutorial 6 : Solving a Cubic Equation (Cardano's Forumlae) [http://www.openwetware.org/images/e/ea/WIKI_Document_Number_6_-_Cardano_Formulae.pdf  Cardano]
** Tutorial 6 : Solving a Cubic Equation (Cardano's Formulae) [http://www.openwetware.org/images/e/ea/WIKI_Document_Number_6_-_Cardano_Formulae.pdf  Cardano]
 
 
 
== Analyses of Dynamic Systems ==


* '''Final Model with E=0'''
== Analyses of Dynamic Systems (Scanned Notes) ==
The final model was complex and depended on 8 independent parameters - 5 after rendering it dimension-less. 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'''
Some parts of the analysis involved some complex calculations that were beyond the scope of the project and consequently the students used my results. My notes on the analysis of both cases (E=0) and  (E>0) will be scanned soon and posted here for anyone willing to check them

Latest revision as of 09:40, 21 September 2006

Overview of my Contribution to IGEM

I have been an Advisor on Dynamic Systems for the IGEM Imperial College Team. As an advisor I have supervised the study by Imperial IGEM students of ever more complex dynamic systems (from the simple Lotka-Volterra [link] to the complex 2D prey-predator model with bounded growths and killings [link]).

Here is an example of Bifurcation Diagram which was obtained by the team during the various analyses.

Specific Contributions

  • Teaching the Basics of Dynamic Systems
  • Generalities
- What is a Dynamic System?
- How do you interpret the parameters of a Dynamic System?
Focus on the Prey-Predator Models
- What is a Steady Point? Why are so Important?
- Why do we study the Jacobian to study Dynamic analysis?
  • Support for Students
  • Support in Mathematics
- Help for Data Analysis (Methods/Implementation)
- Help for Calculations in Study of Dynamic Systems
  • Creation of Tutorials for IGEM Students (see below) including
- Templates for Study of Dynamic Systems
- templates for Presentation of Results

Tutorials

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

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

Analyses of Dynamic Systems (Scanned Notes)

The final model was complex and depended on 8 independent parameters - 5 after rendering it dimension-less. 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

Some parts of the analysis involved some complex calculations that were beyond the scope of the project and consequently the students used my results. My notes on the analysis of both cases (E=0) and (E>0) will be scanned soon and posted here for anyone willing to check them

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