TANG Xiaowei.Stability of periodic solution for a single population differential system with state-dependent impulse[J].Journal of Yanbian University,2016,42(02):99-102,135.
具状态脉冲的单种群微分系统周期解的稳定性
- Title:
- Stability of periodic solution for a single population differential system with state-dependent impulse
- 分类号:
- O175.31
- 文献标志码:
- A
- 摘要:
- 首先利用流转换理论研究了单种群微分系统的轨线走向问题.在此基础上,建立映射结构,给出了具状态脉冲的单种群微分系统周期解稳定性分析的充分条件,克服了系统在脉冲点处不连续的困难,并通过例子说明了结论的有效性.
- Abstract:
- The trajectory direction of a single population differential system is studied through flow switchability theory. By setting up mapping structures, a sufficient condition for the stability of periodic solutions of a single population differential system with state-dependent impulse is given, which overcomes the discontinuous difficulty caused by impulse. At last the effectiveness is verified.
参考文献/References:
[1] Sun Chenlan. Models and Research Methods Of Mathematical Ecology[M]. Beijing: Science Press, 1988:199-231.
[2] 陈兰荪,陈健.非线性生物动力系统[M].北京:科学出版社,1993:215-226.
[3] Jiang Guirong. Complex dynamics of a Holling type II prey-predator system with state feedback control[J]. Chaos, Solutions and Fractals, 2007,31(2):448-461.
[4] 宋新宇,郭红建,师向云.脉冲微分方程理论及其应用[M].北京:科学出版社,2011:208-209.
[5] Zhang Yujuan, Liu Bing, Chen Lansun. Extinction and permanence of a two-prey one-predator system with impulsive effect[J]. IMA Journal of Mathematical Medicine and Biology, 2003,20(4):309-325.
[6] 黄明湛,宋新宇.具有状态反馈脉冲控制的种群互惠动力系统的研究[J].系统科学与数学,2012,32(3):265-276.
[7] Zhao Jingdong, Guo Xin. Average conditions for competitive system in a nonautonomous two dimensional Lotka-Volterra system[J]. Mathematical and Computer Modeling, 2013,57(5):1131-1138.
[8] Luo Albert C J. Discrete and Switching Dynamical System[M]. Beijing: Higher Education Press, 2012:167-204.
相似文献/References:
[1]田德生,朱长青.四阶泛函微分方程周期解的存在性和全局吸引性[J].延边大学学报(自然科学版),2013,39(04):240.
[2]刘东旭,司文艺,袁玉娇.一类单部件可修复系统的稳定性及可靠性分析[J].延边大学学报(自然科学版),2014,40(01):15.
LIU Dongxu,SI Wenyi,YUAN Yujiao.The exponential stability and reliability analysis of a kind of single-component repairable system[J].Journal of Yanbian University,2014,40(02):15.
[3]韩筱爽,方明.具有预警功能和可修复储备部件的人-机系统[J].延边大学学报(自然科学版),2014,40(02):142.
HAN Xiaoshuang,FANG Ming.A human-machine system with warning function and general failed system repair time distribution[J].Journal of Yanbian University,2014,40(02):142.
[4]唐晓伟.基于首次积分和向量场的二维Lotka-Volterra系统的稳定性[J].延边大学学报(自然科学版),2015,41(03):203.
TANG Xiaowei.Stability of a two-dimensional Lotka-Volterra system with first integral and vector field[J].Journal of Yanbian University,2015,41(02):203.
[5]余胜斌.一类离散非自治竞争系统的绝灭性和稳定性[J].延边大学学报(自然科学版),2015,41(04):279.
YU Shengbin.Extinction and stability in a class of discrete non-autonomous competition system[J].Journal of Yanbian University,2015,41(02):279.
[6]吴凡,侯成敏*.分数阶q -对称非自治系统的稳定性[J].延边大学学报(自然科学版),2016,42(03):188.
WU Fan,HOU Chengmin*.Stability of q -symmetric fractional non-autonomous systems[J].Journal of Yanbian University,2016,42(02):188.
[7]余胜斌.具毒素影响的连续型竞争系统的绝灭性和稳定性[J].延边大学学报(自然科学版),2016,42(03):196.
YU Shengbin.Extinction and stability in a continuous competitive system with the effect of toxic substances[J].Journal of Yanbian University,2016,42(02):196.
[8]李晓艳,谢建民.一类高阶有理差分方程的全局行为[J].延边大学学报(自然科学版),2016,42(04):302.
LI Xiaoyan,XIE Jianmin.Global behavior of a higher-order rational difference equation[J].Journal of Yanbian University,2016,42(02):302.
[9]庄科俊.一类含有避难所和扩散项的食物链模型的稳定性[J].延边大学学报(自然科学版),2016,42(04):306.
ZHUANG Kejun.Stability analysis of a food-chain model incorporating prey refuge and diffusive term[J].Journal of Yanbian University,2016,42(02):306.
[10]张志敏.一类非自治差分竞争系统的绝灭性和稳定性[J].延边大学学报(自然科学版),2017,43(02):104.
ZHANG Zhimin.Extinction and stability in a nonautonomous difference competitive system[J].Journal of Yanbian University,2017,43(02):104.
备注/Memo
收稿日期: 2016-04-13 基金项目: 国家自然科学基金资助项目(11571208)作者简介: 唐晓伟(1983—),女,讲师,研究方向为微分方程稳定性.