The Lotka-Volterra predator-prey model

Optimal prey activity
Optimal prey activity:
u(P ) =
{
1 if P < Ps = r 1
λ 1
0 if P > P s
Prey should be active if predator density is below the critical threshold. When above
they should be inactive.
Optimal predator activity:
v(R) =
{
1 if R > Rs = m 2
eλ 2
0 if R < R s
Predators should be active if the benefit from activity overweights the increased
mortality due to predator activity. Otherwise they should be inactive.