模糊微分方程是在模糊环境下研究动态系统的重要工具,所以对方程进行求解是一项必不可少的工作.为了能使更多的模糊微分方程更容易求解,通过对非线性模糊微分方程进行变量替换判断方程是否可约,并在此过程中试图找到非线性模糊微分方程转化成线性模糊微分方程的方法.最后给出了2种形式的模糊微分方程是否可约的充分条件,同时推导出非线性模糊微分方程转化为线性模糊微分方程的具体方法,使可约模糊微分方程更容易辨别和求解,并且给出算例验证了结果的有效性.
Fuzzy differential equation is an important tool for studying dynamic system in fuzzy environment. Therefore, finding the solutions to these equations is essential. In order to make more fuzzy differential equations easier to solve, variables substitution is performed in nonlinear fuzzy differential equation to judge whether the equation is reducible. In this process, we try to find out the method to reduce a nonlinear fuzzy differential equation to a linear fuzzy differential equation. In the last, the conditions of two types of fuzzy differential equations being reducible are given. Therefore, it becomes easy to distinguish reducible fuzzy differential equations and solve them. In addition, some examples are given to verify the effectiveness of the results.
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