The Lotka-Volterra predator-prey model

Population dynamics
dx i
dt = x if i (x, u),
i = 1, . . . , n
Controls (animal strategies, or phenotypic plastic traits):
u = (u 1 , . . . , u k ) ∈ U=U 1 × · · · × U k
Fitness of the i-th individuals:
G i (u i ; u, x) = f i (x, u)
Strategies that maximize animal fitness are the Nash equilibria (or Evolutionary Stable
Strategies) at current population numbers:
N(x) = { u ∈ U | G i (u i ; u, x) ≥ G i (v; u, x) for any v ∈ U i , i = 1, . . . , k } .
Feedback control:
u ∈ N(x)
This approach assumes time scale separtion: Behavioral processes operate on a much
faster time scale than do population dynamics