ALTERNATIVE MODELS FOR CYCLIC LEMMING DYNAMICS

• Main Authors: Hao Wang, Yang Kuang
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Barrow; Point Barrow; Alaska
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.9168; http://math.la.asu.edu/~kuang/paper/WangKuang.pdf

Abstract. Many natural population growths and interactions are affected by seasonal changes. This suggests that these natural population dynamics should be modeled by nonautonomous differential equations instead of autonomous differential equations. Through a series of carefully derived models of the well documented high-amplitude, large-period fluctuations of lemming populations, we argue that when appropriately formulated, autonomous differential equations may capture much of the desirable rich dynamics such as the existence of a periodic solution with period and amplitude close to that of approximately periodic solutions produced by the more natural but mathematically daunting nonautonomous models. We start this series of models from the Barrow model, a well formulated model for the dynamics of food-lemming interaction at Point Barrow (Alaska, USA) with sufficient experimental data. Our work suggests that autonomous system can indeed be a good approximation to the moss-lemming dynamics at Point Barrow. This together with our bifurcation analysis indicate that neither seasonal factor (expressed by time dependent moss growth rate and lemming death rate in Barrow model), nor the moss growth rate and lemming death rate are the main culprits of the observed multi-year lemming cycles. We suspect that main culprits may include high lemming predation rate, high lemming birth rate and low lemming self-limitation rate. 1. Introduction. Pioneer