Hopf Bifurcation of an $(n+1)$ -Neuron Bidirectional Associative Memory Neural Network Model With Delays

2013 ◽  
Vol 24 (1) ◽  
pp. 118-132 ◽  
Author(s):  
Min Xiao ◽  
Wei Xing Zheng ◽  
Jinde Cao
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Associative Memory ◽  
Network Model ◽  
Neural Network Model ◽  
Bidirectional Associative Memory

scholarly journals A Study of Associative Memories with Hopfield neural network Model for handwritten character recognition

2018 ◽  
Vol 3 (01) ◽  
Author(s):  
Sandeep Kumar ◽  
Manu Pratap Singh
Keyword(s):  
Neural Network ◽  
Associative Memory ◽  
Network Model ◽  
Neural Network Model ◽  
Character Recognition ◽  
Hopfield Neural Network ◽  
Recurrent Network ◽  
Associative Memories ◽  
Bidirectional Associative Memory ◽  
Content Addressable Memory

Neural network is the most important model which has been studied in past decades by several researchers. Hopfield model is one of the network model proposed by J.J. Hopfield that describes the organization of neurons in such a way that they function as associative memory or also called content addressable memory. This is a recurrent network similar to recurrent layer of the hamming network but which can effectively perform the operation of both layer hamming network. The design of recurrent network has always been interesting problems to research and a lot of work is going on present application. In present paper we will discuss about the design of Hopfield Neural Network (HNNs), bidirectional associative memory (BAMs) and multidirectional associative memory (MAMs) for handwritten characters recognition. Recognized characters are Hindi alphabets.

scholarly journals Dynamical Behavior in a Four-Dimensional Neural Network Model with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Normal Form Theory ◽  
Form Theory ◽  
Explicit Formulae ◽  
Delay Differential

A four-dimensional neural network model with delay is investigated. With the help of the theory of delay differential equation and Hopf bifurcation, the conditions of the equilibrium undergoing Hopf bifurcation are worked out by choosing the delay as parameter. Applying the normal form theory and the center manifold argument, we derive the explicit formulae for determining the properties of the bifurcating periodic solutions. Numerical simulations are performed to illustrate the analytical results.

STABILITY AND BIFURCATION ANALYSIS ON A DELAYED NEURAL NETWORK MODEL

2005 ◽  
Vol 15 (09) ◽  
pp. 2883-2893 ◽  
Author(s):  
XIULING LI ◽  
JUNJIE WEI
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Delayed Neural Network ◽  
The Stability

A simple delayed neural network model with four neurons is considered. Linear stability of the model is investigated by analyzing the associated characteristic equation. It is found that Hopf bifurcation occurs when the sum of four delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. An example is given and numerical simulations are performed to illustrate the obtained results. Meanwhile, the bifurcation set is provided in the appropriate parameter plane.

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