The cohort feedback model with symmetric net maternity

Demographic cohort feedback models were introduced by Ronald D. Lee in 1974. In these non‐linear models, a cohort's net reproduction ratio responds inversely to cohort size at birth, while the shape of the net maternity function remains constant. For certain response strengths such a model leads to sustained cycles in the trajectory of births. Suppose that the net maternity function is symmetric under reflection around some mean age of childbearing. I prove that the model then has cyclic solutions with period exactly equal to twice the mean age of childbearing not merely in a neighborhood of equilibrium but for a range of parameter values which is unbounded in a certain suitable sense. Sobolev space methods are introduced for the theorem's proof. This “global”; bifurcation theorem for the cohort feedback model with symmetric net maternity provides a benchmark case for understanding the characteristics of non‐linear population waves of realistic size.

Key words:

• Bifurcation
• feedback
• limit cycles
• Sobolev spaces
• non‐linear demography