Turchin模型动力学行为研究

实验室采集的数据都是离散的,且自然界中很多食植动物都是非叠代繁殖的。为了准确解释种群密度的周期振荡现象,Turchin提出离散时间模型。本文利用非线性微分方程的理论知识对Turchin模型的动力学行为进行详尽的分析,探讨解的有界性,得出解的存在范围,从而得到正向不变集;求出边界平衡点并讨论其稳定性;给出内部平衡点的存在条件及其局部渐近稳定的充要条件,为进一步解释种群的动态规律提供理论依据。

Dynamics of Turchin Model

Discrete time series might be more appropriate for studying herbivores with non-overlapping generations, and annual plants. Experimental data are collected periodically, so Turchin prposed a discrete model in May, 2003. In this paper, based on the established Turchin model, the boundedness of solutions is discussed. Positive invariant set is given. Detailed qualitative analysis of the model is carried out, including the existence and stability of equilibrium. The theory can be used to explain the kinetic laws of the population.