Quasi-periodic invariant 2-tori in a delayed BAM neural network

2020 ◽  
Vol 401 ◽  
pp. 193-208
Author(s):  
Xuejing Deng ◽  
Xuemei Li ◽  
Fang Wu
Keyword(s):  
Neural Network ◽  
Bam Neural Network

scholarly journals Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays

2006 ◽  
Vol 2006 ◽  
pp. 1-29 ◽  
Author(s):  
Xiang-Ping Yan ◽  
Wan-Tong Li
Keyword(s):  
Neural Network ◽  
Critical Values ◽  
Multiple Delays ◽  
Multiple Time ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Fourth Degree ◽  
Form Theory ◽  
Bam Neural Network ◽  
The Stability

We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM) neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. 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.

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