Stability and bifurcation analysis in a system of four coupled neurons with multiple delays

被引：0
作者：
Xiu-ling Li
Jun-jie Wei
机构：
[1] Jilin University of Finance and Economics,College of Applied Mathematics
[2] Harbin Institute of Technology,Department of Mathematics
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2013年 / 29卷
关键词：
stability; bifurcation; multiple delays; 34K15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.
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页码：425 / 447
页数：22
相关论文
共 32 条
  • [1] Campbell SA(1999)Qualitative analysis of a neural nerwork model with multiple time delays International J. Bifu. Chaos 9 1585-1595
  • [2] Ruan S(1999)Minimal instability and unstable set of a phaselocked periodic orbit in a delayed neural network Physica D 134 185-199
  • [3] Wei J(2001)Existence and attraction of a phase-locked oscillation in a delayed network of two neurons Differential Integral Equations 14 1181-1236
  • [4] Chen Y(2001)Slowly oscillating oeriodic solutions for a delayed frustrated network of two neurons J. Math. Anal. Appl. 259 188-208
  • [5] Wu J(2000)On a planar system modeling a neuron network with memory J. Diff. Eqs. 168 129-149
  • [6] Chen Y(2001)Biburcation in a planar system of differential delay equations modelling neural activity Physica D 159 215-232
  • [7] Wu J(2005)Stability and bifurcation analysis on a delayed neutal network model Internat. J. Bifur. Chaos 15 2883-2893
  • [8] Chen Y(2007)Global existence of periodic solutions in a four-neuron network model with delays International Journal of Qualitative Theory of Differential Equations and Applications 1 186-200
  • [9] Wu J(2001)Bifurcation analysis on a two-neuron system with distribution delays Physica D 149 123-141
  • [10] Faria T(1997)Temporal dynamics of a two neuron continuous network model with time delay Appl. Math. Modeling 21 673-679
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