State-dependent delay differential equations in population dynamics: Modeling and analysis (Q2738670)

The authors wrote a very readable and timely short survey on state-dependent delay differential population models. As suggested by the authors, most time delays in nature are not constant. The most likely scenarios are that they dependent on the history of the environment which includes the history of food supply and population density. It thus can be argued that population growth models must model food supply explicitly and allow maturation time delay to vary. This, however, can be a challenge. To have plausible and yet tractable models, the authors introduce a nice modification of the model due to Aiello, Freedman and Wu and find more plausible and new dynamics. Specifically, if the maturation time delay depends on the total population at birth, the model can exhibit oscillatory dynamics.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00044].