index Expo Renew Nonrenew 2source Slowren Factors Recycle Daypr

Growth on Internal Limiting Factors


The production of a product is limited by its own recycling products, which are needed for the production process.


  • The recycle of nutrients in a balanced aquarium; nutrients are the limiting factor.
  • Recycle of Chlorophyll
  • Diagram


    I = energy source from outside the system
    TN = total materials available for recycle
    N = storage of recycled material
    P = production of Q
    Q = storage of the product that will be recycled
    F = fraction of Q that is nutrients
    K1, K2 = increasing and decreasing factors of Q


    N = TN - F*Q
    P = K1*I*N
    DQ = P - K2*Q
    P = (K1*K2*TN*I)/(K2 + K1*F*I)


    The graph shows the production of P in function of the source I. (red: entered value of TN. blue: double value of TN)
    Source code:

    "What if" Experiments:

  • What is the effect of increasing the total materials TN available for recycle?
  • What is the effect of increasing the percent of storage Q recycled per unit time?