A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices

2013 ◽  
Vol 92 ◽  
pp. 40-52 ◽  
Author(s):  
Chenfu Yi ◽  
Yunong Zhang ◽  
Dongsheng Guo
Keyword(s):  
Neural Networks ◽  
Real Time ◽  
Recurrent Neural Networks ◽  
Lyapunov Equation ◽  
Time Varying ◽  
Varying Coefficient ◽  
Time Solution ◽  
New Type

Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks

2004 ◽  
Vol 16 (7) ◽  
pp. 1413-1436 ◽  
Author(s):  
Nils Bertschinger ◽  
Thomas Natschläger
Keyword(s):  
Neural Networks ◽  
Real Time ◽  
Recurrent Neural Networks ◽  
Chaotic Dynamics ◽  
Connectivity Matrix ◽  
Time Varying ◽  
Recurrent Networks ◽  
Edge Of Chaos ◽  
Different Types ◽  
Critical Boundary

Depending on the connectivity, recurrent networks of simple computational units can show very different types of dynamics, ranging from totally ordered to chaotic. We analyze how the type of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gates driven by a time-varying input signal depends on the parameters describing the distribution of the connectivity matrix. In particular, we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place. Employing a recently developed framework for analyzing real-time computations, we show that only near the critical boundary can such networks perform complex computations on time series. Hence, this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos, that is, the transition from ordered to chaotic dynamics.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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