✦ LIBER ✦

Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain

✍ Scribed by Xiaofeng Liao; Shaowen Li; Guanrong Chen

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 442 KB
Volume: 17
Category: Article
ISSN: 0893-6080
DOI: 10.1016/j.neunet.2003.10.001

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, a general two-neuron model with distributed delays and a strong kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter for the model is determined. Furthermore, if the mean delay used as a bifurcation parameter, it is found that Hopf bifurcation occurs for the strong kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations are given to justify the theoretical analysis results.

📜 SIMILAR VOLUMES

Frequency domain analysis for bifurcatio

Frequency domain analysis for bifurcation in a simplified tri-neuron BAM network model with two delays

✍ Changjin Xu; Xianhua Tang; Maoxin Liao 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 530 KB

In this paper, a class of simplified tri-neuron BAM network model with two delays is considered. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. If the sum tau of delays tau(1) and tau(2) is c

Stability and bifurcation in a discrete

Stability and bifurcation in a discrete system of two neurons with delays

✍ Shangjiang Guo; Xianhua Tang; Lihong Huang 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 217 KB

A frequency-domain approach to the analy

A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations

✍ F. L. Traversa; F. Bonani; S. Donati Guerrieri 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 514 KB

Effect of delay on the boundary of the b

Effect of delay on the boundary of the basin of attraction in a system of two neurons

✍ K. Pakdaman; C. Grotta-Ragazzo; C.P. Malta; O. Arino; J.-F. Vibert 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 247 KB

The behavior of neural networks may be influenced by transmission delays and many studies have derived constraints on parameters such as connection weights and output functions which ensure that the asymptotic dynamics of a network with delay remains similar to that of the corresponding system witho

Development of a three-phase bus impedan

Development of a three-phase bus impedance matrix in the complex frequency domain for transient analysis in unbalanced distribution systems

✍ Elham B. Makram; Adly A. Girgis 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 685 KB

Untransposed feeders, a combination of single-phase, two-phase and unequal threephase loads impose imbalance in distribution systems. This paper presents a generalized computer technique to develop the threephase bus impedance matrix Zbus3(S) in the complex frequency domain. The method utilizes the

On the Low-frequency Asymptotic Expansio

On the Low-frequency Asymptotic Expansion for some Second-order Elliptic Systems in a Two-dimensional Exterior Domain

✍ Wakako Dan 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 746 KB

## Communicated by Y. Shibata We derive the low-frequency asymptotic expansion of the exterior boundary value problems in two dimensions for second-order elliptic system concerning the theory of elastostatics. As an application of our result, the rate of the local energy decay of solutions of the