Linear stability and Hopf bifurcation in a delayed two-coupled oscillator with excitatory-to-inhibitory connection

被引：11

作者：

Jiang, Yuzhu ^{[1
]}

Guo, Shangjiang ^{[1
]}

机构：

[1] Hunan Univ, Dept Appl Math, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Linear stability; Hopf bifurcation; Normal form; Center manifold; FUNCTIONAL-DIFFERENTIAL EQUATIONS; NEURAL-NETWORKS; DYNAMICS; NEURONS; MODEL;

D O I：

10.1016/j.nonrwa.2009.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the dynamical behavior of a delayed two-coupled oscillator with excitatory-to-inhibitory connection. Some parameter regions are given for linear stability, absolute synchronization, and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. Finally, numerical simulations are given to illustrate the results obtained. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：2001 / 2015

页数：15

共 17 条

[11] A MODEL OF THE NERVE IMPULSE USING 2 1ST-ORDER DIFFERENTIAL-EQUATIONS [J].

HINDMARSH, JL ;

ROSE, RM .

NATURE, 1982, 296 (5853) :162-164

[12] SYNERGISM AND ANTAGONISM OF NEURONS CAUSED BY AN ELECTRICAL SYNAPSE [J].

KAWATO, M ;

SOKABE, M ;

SUZUKI, R .

BIOLOGICAL CYBERNETICS, 1979, 34 (02) :81-89

[13]

KRYUKOV VI, 1990, STOCHASTIC CELLULAR, P225

[14]

MacGregor RI., 1987, NEURAL BRAIN MODELLI

[15] NONLINEAR DYNAMICS AND STABILITY OF ANALOG NEURAL NETWORKS [J].

MARCUS, CM ;

WAUGH, FR ;

WESTERVELT, RM .

PHYSICA D, 1991, 51 (1-3) :234-247

[16] EXCITATORY AND INHIBITORY INTERACTIONS IN LOCALIZED POPULATIONS OF MODEL NEURONS [J].

WILSON, HR ;

COWAN, JD .

BIOPHYSICAL JOURNAL, 1972, 12 (01) :1-&

[17] Symmetric functional differential equations and neural networks with memory [J].

Wu, JH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (12) :4799-4838

← 1 2 →