A birth model with oscillating rate of growth

"Integral equations similar to those generated by the assumption of unchanging vital rates in a closed population leading to eventual stability can be obtained by allowing the rates to vary according to some prescribed rules. In spite of these changing patterns of the vital rates, some of these models have earlier been found to approach stability where the solutions of the stable parameters can be obtained by following the usual straightforward methods. In this paper, a similar integral equation with changing vital rates has been presented which can also be solved in a similar manner. However, the resulting rate of growth does not stabilize but continues to oscillate. The period and amplitude of this oscillating rate of growth together with its central value can be determined from the specified pattern of variation of the vital rates."