IGEM:IMPERIAL/2006/project/modelling template

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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....
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