A mathematical model for the population of giant pandas and bamboo in Yele Nature Reserve of Xiangling Mountains

We describe an improved mathematical model for the relationship between the population of giant pandas (Ailuropoda melanoleuca) and bamboo (Bashania spanostachya) developed by Smith (1979) and Yuan et al. (1989), by adding a correction term which takes into account the effect of a sudden collapse of bamboo as a food source. The values for the co-efficients were based on field data collected in 1994 and 1995 in Yele Nature Reserve (Mianning county, Sichuan Province). The model reflects the dynamic relationship between giant pandas and bamboo in Xiangling Mountains. It is more realistic than earlier models. The density dependent co-efficient for bamboo in the model, Parameter a, decides whether the positive equilibrium point B is a stable or an unstable focus as a changes. The branching value a0 exists in a very narrow interval. The fundamental structure of the phase graph of the model changes significantly and one stable limit cycle is obtained.