Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays

被引：41
|
作者：
Fan, Dejun [1 ,2 ]
Hong, Ling [1 ]
机构：
[1] Xi An Jiao Tong Univ, MOE Key Lab Strength & Vibrat, Xian 710049, Shaanxi, Peoples R China
[2] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Shandong, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2010年 / 15卷 / 07期
基金：
中国国家自然科学基金;
关键词：
FHN model; Time delay; Hopf bifurcation; Stability switch; Periodic solutions; NETWORK MODEL; DIFFERENTIAL EQUATIONS; TIME-DELAY; MEMORY; ZEROS; SYNCHRONIZATION; STABILITY;
D O I：
10.1016/j.cnsns.2009.07.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents an investigation of stability and Hopf bifurcation of the synaptically coupled nonidentical FHN model with two time delays. We first consider the existence of local Hopf bifurcations, by regarding the sum of the two delays as a parameter, then derive explicit formulas for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, using the normal form method and center manifold theory. Finally, numerical simulations are carried out for supporting the theoretical analysis. (c) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：1873 / 1886
页数：14
相关论文
共 50 条
  • [1] HOPF BIFURCATION IN A SYNAPTICALLY COUPLED FHN NEURON MODEL WITH TWO DELAYS
    Zhang, Liping
    Zhou, Ningning
    COMPUTATIONAL INTELLIGENCE: FOUNDATIONS AND APPLICATIONS: PROCEEDINGS OF THE 9TH INTERNATIONAL FLINS CONFERENCE, 2010, 4 : 995 - 1000
  • [2] Stability and Hopf Bifurcation Analysis in Synaptically Coupled FHN Neurons with Two Time Delays
    Fan, Dejun
    Hong, Ling
    DYNAMICAL SYSTEMS: DISCONTINUITY, STOCHASTICITY AND TIME-DELAY, 2010, : 157 - 167
  • [3] Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays
    Dejun Fan
    Ling Hong
    Junjie Wei
    Nonlinear Dynamics, 2010, 62 : 305 - 319
  • [4] Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays
    Fan, Dejun
    Hong, Ling
    Wei, Junjie
    NONLINEAR DYNAMICS, 2010, 62 (1-2) : 305 - 319
  • [5] HOPF-PITCHFORK BIFURCATION ANALYSIS IN A COUPLED FHN NEURONS MODEL WITH DELAY
    Wang, Runxia
    Liu, Haihong
    Yan, Fang
    Wang, Xiaohui
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2017, 10 (03): : 523 - 542
  • [6] Bifurcation and synchronization of synaptically coupled FHN models with time delay
    Wang, Qingyun
    Lu, Qishao
    Chen, GuanRong
    Feng, Zhaosheng
    Duan, Lixia
    CHAOS SOLITONS & FRACTALS, 2009, 39 (02) : 918 - 925
  • [7] Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays
    Karaoglu, Esra
    Yilmaz, Enes
    Merdan, Huseyin
    NONLINEAR DYNAMICS, 2016, 85 (02) : 1039 - 1051
  • [8] Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays
    Esra Karaoğlu
    Enes Yılmaz
    Hüseyin Merdan
    Nonlinear Dynamics, 2016, 85 : 1039 - 1051
  • [9] Stability and Hopf bifurcation of FHN neuron model with time delay under magnetic flow
    Guotai Chen
    Yanhong Zheng
    Qiaoyun Zeng
    Dan Yi
    International Journal of Dynamics and Control, 2023, 11 : 985 - 994
  • [10] Stability and Hopf bifurcation analysis of flux neuron model with double time delays
    Wei, Lixiang
    Zhang, Jiangang
    An, Xinlei
    Nan, Mengran
    Qiao, Shuai
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 68 (06) : 4017 - 4050
12345