scholarly journals Hopf–Pitchfork bifurcation in a simplified BAM neural network model with multiple delays

2013 ◽  
Vol 253 ◽  
pp. 222-234 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Pitchfork Bifurcation ◽  
Multiple Delays ◽  
Bam Neural Network

scholarly journals Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Xiang-Ping Yan ◽  
Wan-Tong Li
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Global Existence ◽  
Periodic Solutions ◽  
Network Model ◽  
Neural Network Model ◽  
Multiple Delays ◽  
Global Hopf Bifurcation ◽  
Existence Of Periodic Solutions ◽  
Bam Neural Network

We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.

CODIMENSION ONE BIFURCATION OF EQUIVARIANT NEURAL NETWORK MODEL WITH DELAY

2010 ◽  
Vol 20 (04) ◽  
pp. 1255-1259
Author(s):  
CHUNRUI ZHANG ◽  
BAODONG ZHENG
Keyword(s):  
Neural Network ◽  
Normal Form ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Double Zero ◽  
Codimension One ◽  
Bam Neural Network ◽  
Manifold Theory ◽  
Form Approach

In this paper, we consider double zero singularity of a symmetric BAM neural network model with a time delay. Based on the normal form approach and the center manifold theory, we obtain the normal form on the centre manifold with double zero singularity. Some numerical simulations support our analysis results.

MULTIPLE BIFURCATION ANALYSIS IN A NEURAL NETWORK MODEL WITH DELAYS

2006 ◽  
Vol 16 (10) ◽  
pp. 2903-2913 ◽  
Author(s):  
YUAN YUAN ◽  
JUNJIE WEI
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Network Model ◽  
Neural Network Model ◽  
Bifurcation Theory ◽  
Center Manifold ◽  
Pitchfork Bifurcation ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Theoretical Results

A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results.

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