一类时滞反应扩散差分系统周期解的稳定性和吸引性  

Stability and Attractability of Periodic Solutions for a Coupled Finite Difference Reaction Diffusion System with Time Delays

作　　者：陈玉娟[1] 刘红[2] 

机构地区：[1]南通大学,江苏南通226007 [2]中国人民解放军镇江船艇学院,江苏镇江212003

出　　处：《南通大学学报（自然科学版）》2009年第2期74-80,共7页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(10571087);江苏省教育厅自然科学计划项目(07KJD110166);江苏省青蓝工程项目;江苏省第二批博士后科研资助计划项目(0702004C);南通大学立项资助项目(08B02;06Z011)

摘　　要：研究了一类周期差分抛物系统时间周期解的存在性、稳定性和吸引性.所考虑的问题包含抛物型方程和常微分方程构成的方程组,时滞可能出现在非线性反应函数和边界条件中.当反应函数和边界条件为局部Lipschitz连续时,利用Brower不动点定理,得到时间周期解的存在性;进一步,当反应函数和边界条件为拟单调时,利用单调迭代方法得到了时间周期解的稳定性和吸引性.The existence, stability, and attractivity of time-periodic solutions for a class of coupled parabolic difference equations in a bounded domain are concerned. A system of parabolic equations and ordinary differential equations is taken into consideration. Time delays may occur in non-linear reaction functions and boundary conditions. By using Brower＇s fixed point theorem we get the existence of time-periodic solutions for a class of locally Lipschitz continuous reaction functions and boundary conditions without any quasimonotone requirement. Meanwhile, by using the monotone iterative scheme we get the stability and attractivity for quasimonotone reaction functions and boundary conditions.

关 键 词：时间周期解 反应扩散系统 渐近稳定性 时滞 吸引性 

分 类 号：O175.26[理学—数学]