3) The predator-prey problem Flashcards
1
Q
What is the Lotka–Volterra model
A
2
Q
What do the parameters in the predator-prey ODE represent
A
a - The rate of growth of the prey population
b - The rate, per unit predator, at which predator P represses growth of the prey population N
c - The rate, per unit prey, at which prey N promotes growth of the predator population P
d - The rate of natural decline (death rate) of the predator population P
.
3
Q
What determines if a solution to a system of linear ODEs is stable or unstable
A
- Stable Solutions: Every solution u(t) is stable if all eigenvalues of B have negative real parts.
- Unstable Solutions: Every solution u(t) is unstable if at least one eigenvalue of B has a positive real part
4
Q
How do the trace and determinant of a linear system determine equilibrium stability
A
- Δ<0: Saddle (unstable)
- Δ>0,Σ<0: Stable
- Δ>0,Σ>0: Unstable
5
Q
How is the community matrix constructed
A
6
Q
How do you derive and verify a constant of motion for a system of ODEs
A
