Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1149.34046
Huang, Chuangxia; He, Yigang; Huang, Lihong; Zhaohui, Yuan
Hopf bifurcation analysis of two neurons with three delays.
(English)
[J] Nonlinear Anal., Real World Appl. 8, No. 3, 903-921 (2007). ISSN 1468-1218

The authors study linear stability and give conditions and direction for Hopf bifurcations in the following system of coupled delay differential equations (two neurons with three delays) \align \dot{x}(t) & = - x(t) +a_{11}f(x(t-\tau)) +a_{12}f(y(t-\tau_1)) ,\\ \dot{y}(t) & = - y(t) +a_{21}f(x(t-\tau_2)) +a_{22}f(y(t-\tau)). \endalign Here $x$ and $y$ are scalar variables corresponding to two neurons, $\tau_j$ denote the transmission delays, $a_{ij}$ are synaptic weights. Additionally, $f(0)=0$ so that the zero solution is the equilibrium, which produces Hopf bifurcations studied.
[Sergiy Yanchuk (Berlin)]
MSC 2000:
*34K18 Bifurcation theory of functional differential equations
34K20 Stability theory of functional-differential equations
34K13 Periodic solutions of functional differential equations

Keywords: Hopf bifurcation; neural network; linear stability

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences