index Drain Logistic Compete Coop Exclus Interact Oscillat Preypred Netprod
Openaq Pulse Saltmrsh Prairie Fire Lagoon Climax Species Specarea

Prey-Predator Oscillation


Regular oscillations exist between prey and predator populations. As the prey population starts growing exponentially, the predator population grows so fast that the number of prey is reduced again. With less to eat, the predator population declines again.
The second model (Daypr) is more realistic. There the relatively unlimited energy source E is replaced with J, the steady renewable energy source of the sun and rain. Also added are a storage, P, of grasses and depreciation of the prey, K6*H.


  • Snowshoe hare and lynx
  • Arctic populations (plants and lemmings)
  • Variables:

    E = Unlimited energy source
    J = Renewable energy source (Kilocal. per m2/Summer)
    H = Herbivores
    C = Carnivores
    P = Storage of grasses
    K6 = Depreciation of the prey


    DP = K0*J - K*P*H
    DH = K1*P*H ( - K6*H ) - K4*H*C
    DC = K5*H*C - K8*C


    The graph shows the changes of H (red), C (blue) and P(green) over a time period.
    Source code:

    "What if" Experiments:


  • Change to a system in a lower/higher latitude where there is more/less sun. What happens to the oscillations?
  • Change the herbivores to species which have shorter lives by increasing their depreciation. What happens to the herbivores and carnivores? What happens to the oscillations? Why is the first peak higher when the depreciation is higher?