Periodic equilibria under periodic harvesting. (English) Zbl 0539.92026

Lazer, A. C.; Sanchez, D. A.

Math. Mag. 57, 156-158 (1984).

A simple deterministic model for the growth of one population which is subject to periodic or seasonal harvesting is given by the ordinary differential equation (1) \(\dot x=g(x)-h(t)\). Here \(x=x(t)\) is the size of the population at time t, g(x) is a smooth function usually of the form xf(x), where f(x) is the per capita rate of growth, and h(t) is a T- periodic function representing the harvesting effect. An interesting question is the following: what is the maximum number of T-periodic solutions equation (1) can have?

MSC:

92D25	Population dynamics (general)
34C25	Periodic solutions to ordinary differential equations