The Discrete Logistic Equation
The discrete logistic equation is a crude model of discrete population growth. For example, it could model a species that has a single mating season so that population numbers are updated annually. There is also an annihilation parameter; if the population exceeds this value, then there will be total extinction the following year. Scaling so that the annihilation parameter is 1 we obtain the difference equation:
Pn+1=kPn(1-Pn), where k is a positive constant.
Try the following constants and initial conditions to see different types of orbits: