A model in a coupled system of simple neural oscillators with delays

Chunrui Zhang; Yazhuo Zhang; Baodong Zheng

doi:10.1016/j.cam.2008.10.048

A model in a coupled system of simple neural oscillators with delays

Chunrui Zhang
, Yazhuo Zhang
, Baodong Zheng^*

^*Corresponding author for this work

School of Mathematics

Northeast Forestry University
Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We consider a coupled system of simple neural oscillators. Using the symmetric functional differential equation theories of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799-4838], we demonstrate the multiple Hopf bifurcations of the equilibrium at the origin. The existence of multiple branches of bifurcating periodic solution is obtained. Then some numerical simulations support our analysis results.

Original language	English
Pages (from-to)	264-273
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	229
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2008.10.048
State	Published - 1 Jul 2009

Keywords

Coupled oscillator
Delay differential equation
Hopf bifurcation
Periodic solution
Stability
Symmetry

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10.1016/j.cam.2008.10.048

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title = "A model in a coupled system of simple neural oscillators with delays",

abstract = "We consider a coupled system of simple neural oscillators. Using the symmetric functional differential equation theories of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799-4838], we demonstrate the multiple Hopf bifurcations of the equilibrium at the origin. The existence of multiple branches of bifurcating periodic solution is obtained. Then some numerical simulations support our analysis results.",

keywords = "Coupled oscillator, Delay differential equation, Hopf bifurcation, Periodic solution, Stability, Symmetry",

author = "Chunrui Zhang and Yazhuo Zhang and Baodong Zheng",

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AU - Zhang, Chunrui

AU - Zhang, Yazhuo

AU - Zheng, Baodong

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Y1 - 2009/7/1

N2 - We consider a coupled system of simple neural oscillators. Using the symmetric functional differential equation theories of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799-4838], we demonstrate the multiple Hopf bifurcations of the equilibrium at the origin. The existence of multiple branches of bifurcating periodic solution is obtained. Then some numerical simulations support our analysis results.

AB - We consider a coupled system of simple neural oscillators. Using the symmetric functional differential equation theories of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799-4838], we demonstrate the multiple Hopf bifurcations of the equilibrium at the origin. The existence of multiple branches of bifurcating periodic solution is obtained. Then some numerical simulations support our analysis results.

KW - Coupled oscillator

KW - Delay differential equation

KW - Hopf bifurcation

KW - Periodic solution

KW - Stability

KW - Symmetry

UR - https://www.scopus.com/pages/publications/65049084441

U2 - 10.1016/j.cam.2008.10.048

DO - 10.1016/j.cam.2008.10.048

M3 - 文章

AN - SCOPUS:65049084441

SN - 0377-0427

VL - 229

SP - 264

EP - 273

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

A model in a coupled system of simple neural oscillators with delays

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Keywords

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