期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

中立型Logistic差分方程的Flip分支 被引量：2

Flip Bifurcation Behavior of Neutral Type Logistic System
下载PDF
导出
摘要 讨论了中立型时滞Logistic差分方程稳定性以及Flip分支存在性;应用Jury判据和特征值理论给出正平衡态局部渐进稳定的充分条件;以种群的内禀增长率为分支参数,运用中心流形定理和分支理论得到了方程Flip分支的存在条件与分支方向;通过举例及数值计算验证了定理条件和结论的一致性. The stability and bifurcation behavior of Flip bifurcation behavior of neutral type discrete Logistic system with time delay are investigated in present work.Firstly,the sufficient conditions for the local asymptotic stability of the positive equilibrium are achieved based on the theory of characteristic value and Jury criterion.Secondly,by choosing the intrinsic rate as the bifurcation parameter and using bifurcation theory and the center manifold theorem,we get that the discrete model undergoes a flip bifurcation at an exceptive value of the bifurcation parameter.Finally,numerical examples carry out to justify the main results in this work.
作者 梁璐莎 陈斯养
机构地区 陕西师范大学数学与信息科学学院
出处 《云南师范大学学报（自然科学版）》 2014年第1期41-47,共7页 Journal of Yunnan Normal University:Natural Sciences Edition
基金 国家自然科学基金资助项目(10871122 11171199) 中央高校基本科研专项基金资助项目(JK201302004 JK201302006)
关键词 中立型 时滞 稳定性 Flip分支 Neutral type Delay stability Flip Bifurcation
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献22

  • 1陈兰荪,宋新宇,陆征一.数学生态学模型与研究方法[M].成都:四川科学技术出版社,2008,8.
  • 2CUSHING J M. Integrodifferential equations and delay models in population dynamics[M]. New York:Springer- Verlag, 1977.
  • 3MURRAY J D. Mathematical Biology[M]. New York..Springer-Verlag, 1989.
  • 4OKUBO A. Diffusion and ecological problems:mathematical models[M]. New York:Springer-Verlag, 1980.
  • 5WRIGHT E M. A nonlinear difference-differential equation[J]. J. Reine Angew. Math, 1955 (194) :66-87.
  • 6SMITH F E. Population dynamics in Daphnia magna and a new model for population growth[J]. Ecology, 1963.(44) .. 651-663.
  • 7GOPALSAMY K,ZHANG B G. On a neutral logistic equation [J]. Dynamics and Stability of Systems, 1988 (2) :183-195.
  • 8FREEDMAN H I,Kuang Y. Stability switches in linear scalar neutral delay equations[J]. Funkcialaj Ekvacioj, 1991 (34) : 187-209.
  • 9GOPALSAMY K. Stability and oscillations in delay differential equations of population dynamics[M]. Dor- drechtKluwer Academic Publishers,1992.
  • 10KUANG Y,On neutral delay two-species LotkwVolterra competitive systems[J]. J. Austral. Math. Soc. Series B,1991 (32):311-326.

二级参考文献84

  • 1李方,陈斯养.一类具有时滞和干扰的广义Logistic模型的Hopf分支问题[J].西北师范大学学报（自然科学版）,2008,44(5):1-6. 被引量：3
  • 2党承林,李永萍,彭明春,廖迎芸.生态系统的可靠性及其稳定性的维持[J].云南大学学报（自然科学版）,2006,28(3):257-261. 被引量：8
  • 3范丽,陈斯养.具有时滞的广义Logistic模型的Hopf分支[J].陕西师范大学学报（自然科学版）,2007,35(1):25-29. 被引量：4
  • 4GopalsamyK, LadasG. Oscillations and global attractivity in amodel ofhematopoiesis [ J ]. Dynamics and Differential quations, 1990(2) : 117 - 132.
  • 5Hassard B, Kazarinoff D, Wan Y. Theory and applications of Hopf bifurcation [ M ]. Cambridge: Cambridge Univers Press, 1981.
  • 6MackeyM C. Osccillation and chaos in physiological control systems [ J ]. Science, 1997,197:287 -289.
  • 7SONG YONG-LI,PENG YA-HONG. Stability and bifurcation analysis on a Logistic model with discrete and distributed delays[J]. Appl Math Comput: 2006,181:1745-- 1757.
  • 8RUAN S. Absolute stability,conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays[J]. Quart Appl Math: 2001,59:159-- 173.
  • 9MA ZHAN-PING, HUO HAI-FENG,LIU CHUN-YING. Stability and Hopf bifurcation analysis on a predator- prey model with discrete and distributed delays[J]. Nonlinear Analysis:2009,10:1160--1172.
  • 10秦元勋,刘玉清,王联.带有时滞的动力量的运动稳定性[M].北京:科学出版社,1963.

共引文献24

同被引文献13

  • 1KULENOVIC M R S,LADAS G,PROKUP N R.A rational difference equation[J].Computers and Mathematics with Applications,2001(41):671-678.
  • 2TANG Guo-mei,HU Li-xia,JIA Xiu-mei.Dynamics of a higher-order nonlinear difference equation[J].Discrete Dynamics in Nature and Society,2010,Article ID 534947.
  • 3JIA Xiu-mei,LI Wan-tong.Boundedness and global attractivity of a higher-order nonlinear difference equation[J].Discrete Dynamics in Nature and Society,2010,Article ID610467.
  • 4DOURAKI M J,DEHGHAN M,MASHREGHI J.Dynamics of the difference equation xn+1=xn+pxn-k xn+q[J].Applied Mathematics and Computation 2008,56(1):186-198.
  • 5DEHGHAN M,MAZROOEI-SEBDANI R.Dynamics of high-order rational difference equation[J].Applied Mathematics and Computation,2006,178:345-354.
  • 6JIA Xiu-mei,HU Liu-xia,LI Wan-hong.Dynamics of a rational difference equation[J].Discrete Dynamics in Nature and Society,2010,Aeticle ID 970720.
  • 7DEHGHAN M,RASTEGAR N.On the global behavior of a high-order rational difference equation[J].Computer Physics Communications,2009,180(6):873-878.
  • 8MOHEBBI A, DEHGHAN M. High - order compact solution of the one-dimensional heat and advection-diffusion equations [ J ]. Applied Mathematical Modelling,2010,34 ( 10 ) :3071 - 3084.
  • 9DING Heng - fei,ZHANG Yu - xin. A new difference shceme with high accuracy and absolute stability for solving convection - diffusion equations[ J ]. Journal of Computational and Applied Mathematics,2009,230 (2) :600- 606.
  • 10李瑞霞,何志庆.微分方程数值解法[M].广州:华南理工大学出版社,2005:38-43.

引证文献2

云南师范大学学报（自然科学版）
2014年 第1期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部