Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi 221005, India.
J Theor Biol. 2011 May 21;277(1):1-6. doi: 10.1016/j.jtbi.2011.01.034. Epub 2011 Feb 3.
The article presents the solutions of Lotka-Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem called the homotopy perturbation method (HPM). By using initial values, the explicit solutions of predator and prey populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical biological model.
本文借助于一种称为同伦摄动法（HPM）的非线性问题的解析方法，给出了具有分数阶时间导数的 Lotka-Volterra 方程的解。利用初始值，推导出了不同特殊情况下捕食者和猎物种群的显式解。数值解表明，仅需几次迭代即可获得准确的近似解。该方法在求解这个历史生物模型时，在效率和简单性方面表现出色。
