WinPP软件在一类捕食-被捕食系统动力学研究中的应用

首先介绍了WinPP软件的概况,然后对具有Hassell-Varley型功能反应的捕食-被捕食模型进行了详尽的理论分析,并利用WinPP软件验证了各平衡点的稳定性.结论表明,边界平衡点一定是鞍点,正平衡点在一定条件下是局部渐近稳定的.这表明该系统不会出现某个种群灭绝的现象,并且在一定条件下两种群会以平衡点形式共存,即该生态系统必然会共存而不会灭绝.这意味着该系统具有良好的生态性质——易于保持生态系统的存在和多样性.数值模拟也展示了WinPP软件在研究非线性动力学方面的重要作用.

The Application of the Software WinPP in Studying the Nonlinear Dynamics of a Class of Predator-prey Model

Firstly the software WinPP is briefly introduced in this paper.Then the predator-prey model with the Hassell-Varley functional response is analyzed in detail.Finally the stability of it's equilibria is simulated by employing the software WinPP.The result implies that the boundary equilibrium must be a saddle one and the positive equilibrium is locally stable under some conditions.This means that there is not the extinction of some population and the two populations coexist in the form of equilibrium under some conditions i.e.the ecological system must coexist and never extinct.It implies that the ecological system has a very good property i.e.easy to keep its existence and biological diversity.The numerical simulation in this paper also displays the importance of the WinPP in studying the nonlinear dynamics.