On a periodic-like behavior of a delayed density-dependent branching process

Most of natural populations seem to be regulated in their sizes in complex ways. Particularly, the sizes of some populations change in time or generation roughly periodically. There are many theoretical studies on such population dynamics. This paper develops stochastic population models for a periodic-like population dynamics. To see the nature of such mechanism, we consider simple models of a delayed density-dependent branching process, and present by numerical simulations how such a branching process shows periodic population changes. The effects of randomly changing stationary environments on the population dynamics are also considered.