Math 130B: Ordinary Differential Equations, part II.
Homework solutions.Below are links to homework solutions; the
topics of the problems are indicated.
- Homework
1. Find null-clines; find stationary points. Plot phase-portraits
and bifurcation diagram.
- Homework
2. Stability of stationary points. Basins of attraction and
Lyapunov-functions. Gradient systems.
- Homework
3. Hamiltonian systems; gradient systems. Some calculus.
- Homework
4. Systems in polar coordinates. Alpha- and omega- limit sets. Limit
cycles. Lyapunov-functions.
- Homework
5. More alpha- and omega-limit sets. Local sections. Periodic
orbits. Linearised systems.
- Homework
6. Period of orbits. Predator-prey systems.
- Homework
7. More predator-prey system. Also generalised competing-species
systems. The Bendixson-Dulac criterion.
- Homework
8. More null-clines and phase-portraits. Convert to polars.
- Homework
9.. Show that this system does not exhibit chaos. Note: These are
not quite done. And not entirely correct either.
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