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.

scholarly journals Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qingsong Liu ◽  
Yiping Lin ◽  
Jingnan Cao ◽  
Jinde Cao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Center Manifold ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Critical Value ◽  
Hopf Bifurcations ◽  
The Stability

The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosingτas bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.

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