General Template for the Analysis of a Dynamic System
- 1.1 Introduce some background about your model
- 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....