Our second midterm will be Wednesday April 2. The test will cover topics from Chapters 3 and 4.
More details will be posted soon, but the main theme is:
Qualitative Analysis of two-dimensional systems in both discrete and continuous time.
A non-exhaustive list of topics includes:
- Biological Modeling concepts
- Age-structured models (e.g., Juvenile-Adult)
- Epidemic models (SIS, SIR, SIRS)
- Multi-species models (Predator-Prey, Niche Competition, Host-Parasitoid)
- Linear Algebra concepts
- Writing dynamical systems as Matrix-Vector equations
- Eigenvalues and Eigenvectors
- Analysis of linear 2d discrete-time systems
- The Jury Conditions for Stability
- Computing Stable Age Structures
- Analysis of nonlinear 2d discrete time systems
- Finding equilibria
- Computing the Jacobian and evaluating at the equilibria to determine stability
- Analysis of linear continuous-time systems
- The Trace-Determinant Plane
- The three forms of general solutions when the eigenvales are 1) real and distinct; 2) real and repeated; 3) complex.
- Analysis of nonlinear continuous-time systems
- Finding equilibria
- Using nullclines to sketch flow in the phase portrait
- Computing the Jacobian and evaluating at the equilibria to classify type
Scott A McKinley 