Two simple models of almost the same population with very different dynamics.
We present our point of view of the controversy regarding complex dynamics of population models. We analyze two nonlinear models of population dynamics which may be used to model the same population, but which display very different dynamics. We prove that Model 1 stays globally asymptotically stable, while Model 2 is known to display instability, oscillations, and apparent period doubting leading to chaos. We also indicate situations in which both models are equivalent. We employ these results to argue that the "complex" behavior of some models may be due to apparently small differences in assumptions.
Kimmel
M
M
Department of Statistics, Rice University, Houston, Texas 77251.
Arino
O
O
D000818:Animals; D002468:Cell Physiological Phenomena; D002477:Cells / Q000166:cytology*; D006801:Humans; D008962:Models, Theoretical; D011157:Population Dynamics