Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function

2001 ◽  
Vol 44 (2) ◽  
pp. 193-200 ◽  
Author(s):  
Jinliang Wang ◽  
Luonan Chen ◽  
Zhujun Jing
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Asymptotical Stability ◽  
Output Function ◽  
Input Output

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].

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