Nedorezov L V, Volkova E V
Zh Obshch Biol. 2005 Nov-Dec;66(6):484-90.
The authors propose new type of models with non-overlapping generations. It is assumed that during winter period individuals are not active (as, for example, in insect populations in boreal forests) and some portion of population dyes. However the portion of population, that survives, Q, indirectly depends on feeding conditions in previous growing season. In the formal terms, Q = Q(u) is a decreasing function of the mean population size u (i.e., of the integral) over the growing period, and traditional discrete-time model therefore turns into a discrete-continuous one. Under any constant birth rate Y, the model is reduced to a discrete one in its general form, and a general result consists in global stability of the zero solution for any Y < 1, e.t., in population extinction from any initial state. In particular cases of dependence of Q(u) and different types of population self-limitation during growing season the general model results in a great variety of discrete models (including well known Moran-Ricker and Skellam models). For logistic growth of population during the growing season and exponential decrease in Q(u), the condition is obtained for a non-trivial steady state to exist, and the outcome is presented for bifurcation analysis with regard to parameter Y: cycles with typical period-doubling and chaotic dynamics.
