自然资源环境系统的突变机制

从宏观角度出发，建立了自然资源环境系统的动力学模型，并对模型所反映的突变性质及其经济意义进行了分析。通过考察自然资源与环境污染之间的一种特定耦合关系，建立了资源环境二维动力学模型。经过定态分析，结果表明该模型的突变特征可以归为燕尾型突变。并由分叉点集在经济活动参数空间中的投影，分析了经济活动参数变化与动力系统定态跃迁之间的关系。选取特定的经济活动参数进行动态模拟，结果显示，如要避免动力系统的灾变，相关政策调控参数必须满足一定条件，治理时刻必须早于某个临界值。

On the Mechanism of Catastrophic Shift in Natural Resource and Environmental System

A dynamic model of natural resource and environmental system is developed on a macro level, and its catastro- phic characteristics as well as relevant economic meanings are analyzed. By considering a specific coupling relation between natural resource and environment pollution, a two-dimensional dynamic model is built. The equilibria analysis reveals that the catastrophic feature could be classified as swallowtail catastrophe. The relation between the change in parameters of economic activities and the equilibrium transition of the dynamic model is also discussed with the projection of bifurcation sets onto economic parameter space. The Simulation under given specific change mode of economic activities parameters shows that the related policy parameters have to satisfy some requirements to avoid such catastrophic shift, for example, the abatement time should be earlier than some critical moment.