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....