Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays

2018 ◽  
Vol 149 ◽  
pp. 69-90 ◽  
Author(s):  
Changjin Xu
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Associative Memory ◽  
Bifurcation Analysis ◽  
Multiple Delays ◽  
Bidirectional Associative Memory ◽  
Global Hopf Bifurcation

STABILITY AND BIFURCATION OF BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DELAYED SELF-FEEDBACK

2005 ◽  
Vol 15 (07) ◽  
pp. 2145-2159 ◽  
Author(s):  
LIN WANG ◽  
XINGFU ZOU
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Global Stability ◽  
Numerical Simulations ◽  
Associative Memory ◽  
Bifurcation Analysis ◽  
The Self ◽  
Hopf Bifurcations ◽  
Bidirectional Associative Memory ◽  
Delay Dependent

Some delay independent and delay dependent conditions are derived for the global stability of the bidirectional associative memory neural networks with delayed self-feedback. Regarding the self-connection delay as the parameter to be varied, the linear stability and Hopf bifurcation analysis are carried out. An algorithm to determine the direction and stability of the Hopf bifurcations is also worked out. Some examples and numerical simulations are presented.

Global Stability and Bifurcation in Delayed Bidirectional Associative Memory Neural Networks With an Arbitrary Number of Neurons

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Elham Javidmanesh
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Hopf Bifurcation ◽  
Global Stability ◽  
Associative Memory ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory ◽  
Numerical Examples ◽  
Bam Neural Network ◽  
General Method

In this paper, delayed bidirectional associative memory (BAM) neural networks, which consist of one neuron in the X-layer and other neurons in the Y-layer, will be studied. Hopf bifurcation analysis of these systems will be discussed by proposing a general method. In fact, a general n-neuron BAM neural network model is considered, and the associated characteristic equation is studied by classification according to n. Here, n can be chosen arbitrarily. Moreover, we find an appropriate Lyapunov function that under a hypothesis, results in global stability. Numerical examples are also presented.

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