Lokta-Volterra生态模型的同伦分析解法

Homotopy Analysis Solution to Lokta-Volterra Ecological Model

由于Lokta-Volterra生态模型为非线性模型,无法获得解析解。利用同伦分析方法,得到了该模型解的近似展开式。同伦分析方法不同于其他解析近似方法,该方法提供了一个简单途径,确保所得到的级数解收敛,从而可以获得非线性问题足够精度的解析近似。对近似解与数值解进行了比较,结果表明,近似解具有较高的精度,该方法用于生态模型研究是可行的。

Lokta-Volterra ecological model was considered. It is impossible to get its analytical solution because of nonlinearity. Using the homotopy analysis method, the approximation of the solution for the model was obtained. Different from other analytical techniques it provides us a simple way to ensure the convergence of solution series, so that one can get accurate enough analytical approximations. Compared to the numerical solution, the approximation solution from the method was agreement well with the numerical solution. It shows the method is feasible to studying Lokta-Volterra ecological model.