IGEM:IMPERIAL/2006/project/modelling template

General Template for the Analysis of a Dynamic System

1 Generalities

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

• 1.2 Describe the goals of your study

2 Model description

• 2.1 Write down the set of ODEs characterizing your model
• 2.2 Describe in a table the signification of each term and parameter of the model
  • Use simple terms
  • Give Physical Interpretation when possible
• 2.3 Define strengths and flaws of the model
  • Insist on physical interpretation
  • Look into relevance of model for small numbers

3 Stability analysis

• 3.1 Studying the steady points
  • What is a steady point?
  • What is the property of the system at these particular points ?
  • Write down the set of ODEs to solve to find them
  • Write down their expression.
  • Any remarks on them ?

• 3.2 Studying the stability of the steady points
  • What is the meaning of this study ?
  • Why do we use the Jacobian ?
  • Why do we use its Eigenvalues?
  • What is the rule for stability?
  • Analyse each steady point
    • by writing the value of the Jacobian at this particular point
    • by writing the trace and determinant of the 2D matrix
    • by writing down the eigen values
    • Conclude on the stability of the point considered in regards to the parameters

• 3.3 Studying the Vector Field (VF)
  • What is the Vector Field?
  • Depending of the value of the parameters, define different cases (different behaviours of the steady points)
    • for each case, draw the VF and place the steady points with the behaviour of the flow at their vecinity
    • Plot in the VF, dx/dt=0 and dy/dt=0. By using the sign the dx/dt and dy/dt, draw the general trend of the VF in each region of the VF.
    • Simulate the VF for a few well chosen values of your parameters, justify choice.
    • Plot Different trajectories for wel chosen initial values

• 3.4 General Remarks on the VF
  • Give as thorough as possible an analysis of the VF
  • In particular Focus on
    • Shape of Trajectories
    • Influence of initial conditions
    • Influence of model parameters
  • Make predictions and suggestions regarding the sensitivity analysis
    • NB: Quting Poincare-Bendixson is a bonus for a 2D model....