种群离散Lotka-Volterra模型的精确解

The Exact Solution to Discrete Population Model of Lotka-Volterra

非线性生态数学离散模型的持续生存性和全局稳定性等动力学的研究中,大多学者采用建立LiaPunov函数或者对特定模型进行直接分析以及数值模拟等方式,仅能较为普遍地刻画生态系统的一般性。选用差分方程更能准确地描述种群性态,因此将差分多项式系统的吴方法应用于两种群离散Lotka-Volterra模型的精确求解,并对所得解结构进行分析,为生态学研究提供可靠依据,即分析随着时间的推移种群是持续生存还是走向灭绝。

In the study of persistence and global stability dynamics of nonlinear ecological mathematical discrete model, most researchers established the LiaPunov function or made direct analysis and numerical simulation of specific model, only get the general description of ecological system. The differential equation can describe the population state, which can be used in the discrete population model of Lotka-Volterra.