mathematical example meaning in English

数学例题

Each chapter of the paper reads as follows . firstly , the uniform persistence of the system is proved ; secondly , by using the independent subsystem method , the more brief sufficient conditions for the existence and global attractivity of the periodic solution and a mathematical example is obtained to show its practicality . finally , the conditions of the existence of the positive almost periodic solution which is uniformly asymptotically stable are derived by the razumikhin function method and a mathematical example is obtained
在本文中，首先对于这两类模型，分别考虑各种群的一致持久性；通过对独立子系统的讨论得到了，当系统是周期系统时，周期正解的存在唯一和全局吸引性，当系统是概周期系统时，正概周期解的存在性和一致渐近稳定的条件，并对上述两种情况分别给出了说明其可行性的数学例子。
In chapter one , model ( 1 . 1 . 1 ) is considered ; in chapter two , model ( 2 . 1 . 1 ) is considered , then mathematical examples are given to show their practical respectively ; in chapter three , through comparison of the conditions of ( 1 . 1 . 1 ) and ( 2 . 1 . 1 ) , which gurantee the same results , many interesting results are obtained
1 ) ；在两章中分别给出系统的一致持久性、保证周期解和概周期解的存在唯一性及其相应稳定性的条件，并给出了保证其可行性的数学例子；第三章通过比较模型( 1