On Control of Hopf Bifurcation in BAM Neural Network with Delayed Self-feedback

2006 ◽  
pp. 285-290 ◽  
Author(s):  
Min Xiao ◽  
Jinde Cao
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Bam Neural Network

scholarly journals Effect of Leakage Delay on Hopf Bifurcation in a Fractional BAM Neural Network

2019 ◽  
Vol 29 (06) ◽  
pp. 1950077 ◽  
Author(s):  
Jiazhe Lin ◽  
Rui Xu ◽  
Liangchen Li
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Experimental Studies ◽  
Rank Correlation ◽  
Correlation Coefficients ◽  
Leakage Delay ◽  
Scatter Plots ◽  
Bam Neural Network ◽  
Pass Through ◽  
The Impact

Recently, experimental studies show that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we introduce temporal fractional derivatives into a six-neuron bidirectional associative memory (BAM) neural network with leakage delay. By selecting two different bifurcation parameters and analyzing corresponding characteristic equations, it is verified that the delayed fractional neural network generates Hopf bifurcation when the bifurcation parameters pass through some critical values. In order to measure how much is the impact of leakage delay on Hopf bifurcation, sensitivity analysis methods, such as scatter plots and partial rank correlation coefficients (PRCCs), are introduced to assess the sensitivity of bifurcation amplitudes to leakage delay. Numerical examples are carried out to illustrate the theoretical results and help us gain an insight into the effect of leakage delay.

Stability and global Hopf bifurcation for neutral BAM neural network

2014 ◽  
Vol 145 ◽  
pp. 122-130 ◽  
Author(s):  
Ming Liu ◽  
Xiaofeng Xu ◽  
Chunrui Zhang
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Global Hopf Bifurcation ◽  
Bam Neural Network

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 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.

Sign in / Sign up

Export Citation Format

Share Document