Global Hopf-bifurcation in a neural netlet

被引:33
作者
Gopalsamy, K [1 ]
Leung, IKC [1 ]
Liu, PZ [1 ]
机构
[1] Flinders Univ S Australia, Dept Math & Stat, Adelaide, SA 5001, Australia
关键词
D O I
10.1016/S0096-3003(97)10087-X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Sufficient conditions are obtained for the global Hopf-bifurcation of periodic solutions in the dynamics of a neural netlet of activation and inhibition with continuously distributed delays. The orbital asymptotic stability of the bifurcating periodic solutions is investigated.The results are illustrated with numerical simulations. A few problems are formulated in the form of conjectures. (C) 1998 Elsevier Science Inc. All rights reserved.
引用
收藏
页码:171 / 192
页数:22
相关论文
共 16 条
[1]   GLOBAL BIFURCATIONS OF PHASE-LOCKED OSCILLATORS [J].
ALEXANDER, JC ;
AUCHMUTY, G .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 93 (03) :253-270
[2]   GLOBAL BIFURCATIONS OF PERIODIC ORBITS [J].
ALEXANDER, JC ;
YORKE, JA .
AMERICAN JOURNAL OF MATHEMATICS, 1978, 100 (02) :263-292
[3]  
Chow S-N., 2012, METHODS BIFURCATION
[4]   FULLER INDEX AND GLOBAL HOPF BIFURCATION [J].
CHOW, SN ;
MALLETPARET, J .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1978, 29 (01) :66-85
[5]  
FIEDLER B, 1988, LECT NOTES MATH, V1309
[6]   AN INDEX OF FIXED POINT TYPE FOR PERIODIC ORBITS [J].
FULLER, FB .
AMERICAN JOURNAL OF MATHEMATICS, 1967, 89 (01) :133-&
[7]   Delay induced periodicity in a neural netlet of excitation and inhibition [J].
Gopalsamy, K ;
Leung, I .
PHYSICA D, 1996, 89 (3-4) :395-426
[8]  
Gopalsamy K., 2013, Stability and Oscillations in Delay Differential Equations of Population Dynamics, V74
[9]  
Hassard BD, 1981, LONDON MATH SOC LECT, V41, DOI DOI 10.1090/CONM/445
[10]  
Iooss G., 1990, Elementary Stability and Bifurcation Theory, V2nd