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| 具有时滞的离散互惠系统的周期解 |
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| 引用本文： | 徐昌进,陈大学 .具有时滞的离散互惠系统的周期解 [J].重庆师范大学学报(自然科学版),2012(1):49-55. |
| 作者姓名： | 徐昌进 陈大学 |
| 作者单位： | 贵州财经学院经济系统仿真重点实验室;湖南工程学院理学院 |
| 基金项目： | 国家自然科学基金(No.10771215);贵州财经学院博士科研启动项目(2010);湖南省教育厅资助科研项目(No.10C0560);湖南省科技计划资助项目(No.2010FJ6021) |
| 摘 要： | 本文研究了一类散互惠系统x(k+1)=x(k)expr1(k)(1-(x(k-τ(k)))/(k1(k)))+a(k)y(k)] y(k+1)=y(k)expr2(k)(1-(y(k-τ(k)))/(k2(k))+b(k)x(k)],,运用迭合度和与其相关的连续性定理及先验估计,得到了系统存在正周期解的易于验证的充分条件,也就是,若下列条件i)ri(i=1,2),kj(j=1,2),a,b:Z→R+是ω周期的;ii)aL>(r1/k1)M,bL>(r2/k2)M;iii)rL1>aMkM1满足,则系统至少有一个正的ω周期解,所得结果是前人工作的重要的补充。 |
| 关 键 词： | 离散互惠系统 时滞 迭合度 周期解 |
Periodic Solutions for a Discrete Mutual System with Delays |
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| XU Chang-jin,CHEN Da-xue .Periodic Solutions for a Discrete Mutual System with Delays [J].Journal of Chongqing Normal University:Natural Science Edition,2012(1):49-55. |
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| Authors: | XU Chang-jin CHEN Da-xue |
| Institution: | 1.Guizhou Key Laboratory of Economics System Simulation,Guizhou College of Finance and Economics,Guiyang 550004;2.Faculty of Science,Hunan Institute of Engineering,Xiangtan Hunan 411004,China) |
| Abstract: | In this paper,a discrete-time mutual system x(k+1)=x(k)expr1(k)(1-(x(k-τ(k)))/(k1(k)))+a(k)y(k)]y(k+1)=y(k)expr2(k)(1-(y(k-τ(k)))/(k2(k))+b(k)x(k)],is considered.By using coincidence degree and the related continuation the orem as well as prior estimates,easily verifiable sufficient conditions for the existence of positive periodic solutions are obtained,i.e.,if the following conditions i) ri(i=1,2),kj(j=1,2),a,b:Z→R+ are ω periodic;ii) aL>(r1/k1)M,bL>(r2/k2)M;iii)rL1>aMkM1 hold,then system has at least an ω periodic solution.Our results are important complement to earlier results in the literature. |
| Keywords: | discrete mutual system time delay coincidence degree periodic solution |
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