IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/Template Results

Template for the Analysis of a Dynamical System

Foreword on the template

This template details what is expected of Imperial IGEM students for the presentation of the most important results of the analysis. You may of course adapt the template to your own needs - for instance if you have only one steady points there is no point in showing a bifurcation diagram.

When you write the 'result page' of a model of a Dynamical Systems, please remember the following principles:

- Give the Important Results Only

- Important Simulations must have their Own Page

- Save all Proofs and Extended Discussions for the Attachments (see Appendices)

- Do Not Write Big Paragraphs (Use Bullet Points if Possible)

- Make this document as graphic as possible!! A picture is worth a thousand words...

PS: You should be able to prove the results on display yourself. If you can't prove one of the results , please give credit for the result to whoever has provided you with it.

Introduction

• Introduce some background about your model
  • References
  • Application
  • Relevance of the Model for your Project?
  • Basic Assumptions of the Model

• Model description
  • Write down the set of ODEs characterizing your model
    • Describe the signification of each term and parameter of the model
    • Use simple terms
    • Give Physical Interpretation when possible
  • Define strengths and flaws of the model
  • Insist on physical interpretation

Dimensionless Version of the System

• Give dimensionless equations if you decide to use the dimensionless version of the system
• Give expression of new parameters as a function of the old parameters

Basic Results on the Steady Points and Vector Field

• Results on Steady Points
  • Conditions of Existence
  • Give Coordinates if Possible
  • Sum up Results in one or more Bifurcation Diagram(s)

• If Possible Sketch the Vector Field
  • Sketch can be basic
  • Sketch for Every Zone of the Bifurcation Diagram

Results at Infinity

• Conditions for Trajectories to be Bounded
• If Trajectories do not stay bounded, give Equivalent at Infinity
• If possible: Give Explicit Equations for Trajectories

Results of Dynamic Analysis

• Nature of Steady Points
• Update Bifurcation Diagrams
• Insert Link to Relevant Simulation for Every Interesting Zone of the Bifurcation Diagram
  • You can insert a thumbnail if you wish in the Result Page
  • Every Simulation has its own Wiki Page
  • Insert Qualitative Comments on Simulations
  • Detailed Quantitative Analyses of Simulations a Bonus
  • Sensitivity analysis a bonus
    • Influence of initial conditions
    • Influence of model parameters

Conclusion

• Give Summary of Results
  • Insist on most useful/important properties
  • Also insist on unusual/pathological properties

• Focus on the Problem of Oscillations
  • Condition(s) to obtain a limit cycle
  • If possible: Summary of the qualities of the limit cycle
  • If possible: Make recommendations
    • Some kinds of limit cycles may be more desirable than other
    • What set of parameters do they correspond to ?

• Give Physical Interpretations of Results
  • Focus on differences between model and models studied previously and draw lessons from them
  • If possible: Make links with IGEM experiments

Appendices

• Detailed Study(ies)
  • Attach here all the documents detailing your study of the Dynamical System
  • Ideally document(s) should include basic proofs for the most important resulti
  • If possible use formats like doc or pdf.
• Further Simulations
  • Only the most relevant simulations should be made WIKI-friendly.
  • The rest of the simulations may be attached to the detailed studies attached above.
  • If you want to be really complete , please create a document compiling all your simulations and attach it here
• Computer Code
  • Please make your Matlab code available here
  • If possible include documentation on the code
  • At the very least make sure your code is easy to read and well-commented