中文摘要：

利用微分不等式方法研究一类生物数学中的非线性3种群捕食-被捕食模型的反应扩散系统奇摄动问题．在适当的条件下，利用微分不等式理论，讨论了一个初始边值问题解的存在性和渐近性态．微分不等式理论的实质是构造两个辅助函数作为系统的上、下解．然后使上、下解分别满足相应的不等式．最后证明所研究的系统存在解并处在上、下解之间．从而证明了系统解的存在性，并同时得到解的估计．

英文摘要：

A class of nonlinear three species in the biomathematics is considered with the prey-predator singularly perturbed problems for the reaction diffusion system method of differential inequalities. Under suitable conditions, the existence and asymptotic behavior of solution for the initial boundary value problems are studied with the theory of differential inequalities. The theory of differential inequalities is really to constructing two auxiliary functions, which are super and lower solutions of the system respectively. And then the super and lower solutions are satisfied corresponding inequalities. Finally, there is a solution of the system between the super solution and lower solution. Then the existence of the solution for the system is proved and the asymptotic estimation is obtained.