S-Shaped growth curve
When a species is introduced into a new habitat, the population grows exponentially until the individuals become numerous. The further increase in their number is checked by the environmental resistance factors that the population growth declines until zero population growth is reached. (i.e. constant) and it becomes stable (K). Such curves are called sigmoid curves.
The study of growth curves in S-shaped growth pattern is a self-limiting one where the rate of growth is more and more as density increases. If the limitation is linearly proportional to density we get a symmetrical S-curve so as to approach upper level or limit-K, the carrying capacity. This pattern enhances stability as population regulates itself. Actually
the density often overshoots or is more than K and because of time lags in feedback control resulting in oscillations.