Assuming that a population is not stable but converging rapidly towards stability, while its instantaneous birth and death rates being density dependent, one of the useful stochastic models ...

S-shaped curve: The population initially grows exponentially, but as it approaches carrying capacity, the growth rate slows ...

We develop a new discrete-time model, called the boundary-layer model, to describe the dynamics of single species that have a capacity for fast growth at very low population densities. The model ...