Stability analysis of almost periodic solutions for delayed neural networks without global Lipschitz activation functions

2011 ◽  
Vol 81 (11) ◽  
pp. 2440-2455 ◽  
Author(s):  
Jun Zhou ◽  
Weirui Zhao ◽  
Xiaohong Lv ◽  
Huaping Zhu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Activation Functions ◽  
Delayed Neural Networks

Multiple Almost Periodic Solutions in Nonautonomous Delayed Neural Networks

2007 ◽  
Vol 19 (12) ◽  
pp. 3392-3420 ◽  
Author(s):  
Kuang-Hui Lin ◽  
Chih-Wen Shih
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Contraction Mapping Principle ◽  
Time Lags ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neuron Network ◽  
Delayed Neural Networks ◽  
External Bias ◽  
Exponentially Stable

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.

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