An analytical solution for a nonlinear time-delay model in biology
An analytical solution for a nonlinear time-delay model in biology
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DOI：
10.1016/j.cnsns.2008.11.003
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发表时间：
2009-07
影响因子：
3.9
通讯作者：
H. Khan;S. Liao;R. Mohapatra;K. Vajravelu
中科院分区：
文献类型：
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作者：
H. Khan;S. Liao;R. Mohapatra;K. Vajravelu
本文利用同伦分析方法，建立了非线性时滞微分方程的一种解析方法。以生物学中的一个非线性模型为例，说明了这种分析方法的基本思想。与其他分析方法不同的是，同伦分析方法提供了一种简单的方法来保证解的收敛性，从而总是可以得到精确的近似。定义了一种新的间断函数，以便于符号计算的方式表示时滞微分方程的分段连续解。研究发现，时滞对时滞非线性微分方程的解有很大的影响。该方法具有普遍意义，可用于求解其它非线性时滞问题。
In this paper, the homotopy analysis method is applied to develop a analytic approach for nonlinear differential equations with time-delay. A nonlinear model in biology is used as an example to show the basic ideas of this analytic approach. Different from other analytic techniques, the homotopy analysis method provides a simple way to ensure the convergence of the solution series, so that one can always get accurate approximations. A new discontinuous function is defined so as to express the piecewise continuous solutions of time-delay differential equations in a way convenient for symbolic computations. It is found that the time-delay has a great influence on the solution of the time-delay nonlinear differential equation. This approach has general meanings and can be applied to solve other nonlinear problems with time-delay.