A new input-output function for binary hopfield neural networks

1999 ◽  
pp. 311-320 ◽  
Author(s):  
Gerhard Galán ◽  
Juris Muñoz
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Output Function ◽  
Input Output

Functionally Equivalent Feedforward Neural Networks

1994 ◽  
Vol 6 (3) ◽  
pp. 543-558 ◽  
Author(s):  
Věra Kůrková ◽  
Paul C. Kainen
Keyword(s):  
Neural Networks ◽  
Feedforward Neural Networks ◽  
Activation Function ◽  
Output Function ◽  
Input Output ◽  
General Activation ◽  
Hidden Layer

For a feedforward perceptron type architecture with a single hidden layer but with a quite general activation function, we characterize the relation between pairs of weight vectors determining networks with the same input-output function.

TOPOLOGICAL STRUCTURE OF CHAOS IN DISCRETE-TIME NEURAL NETWORKS WITH GENERALIZED INPUT–OUTPUT FUNCTION

2001 ◽  
Vol 11 (07) ◽  
pp. 1835-1851 ◽  
Author(s):  
JINLIANG WANG ◽  
ZHUJUN JING
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Sigmoid Function ◽  
Output Function ◽  
Input Output ◽  
Attracting Set ◽  
The Neural Networks ◽  
Searching Ability

By analogue of [Chen & Aihara, 1995, 1997, 1999], we theoretically investigate the topologically chaotic structure, attracting set and global searching ability of discrete-time recurrent neural networks with the form of [Formula: see text] where the input–output function is defined as a generalized sigmoid function, such as vi = tanh (μiui), [Formula: see text] and [Formula: see text], etc. We first derive sufficient conditions of existence for a fixed point, and then prove that this fixed point eventually evolves into a snap-back repeller which generates chaotic structure when certain conditions are satisfied. Furthermore we prove that there exists an attracting set which includes not only the homoclinic orbit but also the globally unstable set of fixed points, thereby ensuring the neural networks to have global searching ability. Numerical simulations are also provided to demonstrate the theoretical results. The results indicated in this paper can be viewed as an extension of the works of [Chen & Aihara, 1997, 1999] and others [Gopalsamy & He, 1994; Wang & Smith, 1998].

scholarly journals Inequalities and pth moment exponential stability of impulsive delayed Hopfield neural networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yutian Zhang ◽  
Guici Chen ◽  
Qi Luo
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Hopfield Neural Networks ◽  
New Method ◽  
Integral Inequalities ◽  
Delay Function ◽  
Pth Moment Exponential Stability ◽  
Moment Exponential Stability

AbstractIn this paper, the pth moment exponential stability for a class of impulsive delayed Hopfield neural networks is investigated. Some concise algebraic criteria are provided by a new method concerned with impulsive integral inequalities. Our discussion neither requires a complicated Lyapunov function nor the differentiability of the delay function. In addition, we also summarize a new result on the exponential stability of a class of impulsive integral inequalities. Finally, one example is given to illustrate the effectiveness of the obtained results.

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