Alternative models for cyclic lemming dynamics - Hao Wang; Yang Kuang (Mathematical Biosciences and Engineering)
Many natural population growths and interactions are affected byseasonal changes, suggesting that these natural population dynamicsshould be modeled by nonautonomous differential equations instead ofautonomous differential equations. Through a series of carefullyderived models of the well documented high-amplitude, large-periodfluctuations of lemming populations, we argue that whenappropriately formulated, autonomous differential equations maycapture much of the desirable rich dynamics, such as the existenceof a periodic solution with period and amplitude close to that ofapproximately periodic solutions produced by the more natural butmathematically daunting nonautonomous models. We start this seriesof models from the Barrow model, a well formulated model for thedynamics of food-lemming interaction at Point Barrow (Alaska, USA)with sufficient experimental data. Our work suggests that anautonomous system can indeed be a good approximation to themoss-lemming dynamics at Point Barrow. This, together with ourbifurcation analysis, indicates that neither seasonal factors(expressed by time-dependent moss growth rate and lemming death ratein the Barrow model) nor the moss growth rate and lemming death rateare the main culprits of the observed multi-year lemming cycles. Wesuspect that the main culprits may include high lemming predationrate, high lemming birth rate, and low lemming self-limitation rate.