Log-Domain Circuit Techniques for Nonlinear Neural Networks with Complex Dynamics

2004 ◽  
pp. 229-251
Author(s):  
T. Serrano-Gotarredona ◽  
R. Serrano-Gotarredona ◽  
B. Linares-Barranco
Keyword(s):  
Neural Networks ◽  
Complex Dynamics ◽  
Circuit Techniques ◽  
Log Domain ◽  
Nonlinear Neural Networks

On Some Dynamical Properties of Randomly Connected Higher Order Neural Networks

2013 ◽  
pp. 333-363
Author(s):  
Hiromi Miyajima ◽  
Noritaka Shigei ◽  
Shuji Yatsuki
Keyword(s):  
Neural Networks ◽  
Statistical Method ◽  
Complex Dynamics ◽  
Higher Order ◽  
State Model ◽  
Macroscopic Properties ◽  
Higher Order Neural Networks ◽  
Dynamical Properties ◽  
Model C ◽  
Convenient Model

This chapter presents macroscopic properties of higher order neural networks. Randomly connected Neural Networks (RNNs) are known as a convenient model to investigate the macroscopic properties of neural networks. They are investigated by using the statistical method of neuro-dynamics. By applying the approach to higher order neural networks, macroscopic properties of them are made clear. The approach establishes: (a) there are differences between stability of RNNs and Randomly connected Higher Order Neural Networks (RHONNs) in the cases of the digital state -model and the analog state model; (b) there is no difference between stability of RNNs and RHONNs in the cases of the digital state -model and the analog state -model; (c) with neural networks with oscillation, there are large differences between RNNs and RHONNs in the cases of the digital state -model and the analog state -model, that is, there exists complex dynamics in each model for ; (d) behavior of groups composed of RHONNs are represented as a combination of the behavior of each RHONN.

Stability of a class of directionally sensitive asymmetric nonlinear neural networks

1996 ◽  
Vol 9 (4) ◽  
pp. 555-565 ◽  
Author(s):  
S.P. Tonkin ◽  
R.B. Pinter ◽  
B. Nabet
Keyword(s):  
Neural Networks ◽  
Nonlinear Neural Networks

HARMONIC BALANCE APPROACH TO PREDICT PERIOD-DOUBLING BIFURCATIONS IN NEARLY SYMMETRIC CNNs

2003 ◽  
Vol 12 (04) ◽  
pp. 435-459 ◽  
Author(s):  
MAURO DI MARCO ◽  
MAURO FORTI ◽  
ALBERTO TESI
Keyword(s):  
Neural Networks ◽  
Computer Simulations ◽  
Harmonic Balance ◽  
Recent Literature ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Third Order ◽  
Small Perturbations ◽  
Basic Issue ◽  
Period Doubling Bifurcations

This paper further investigates a basic issue that has received attention in the recent literature, namely, the robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominal symmetric interconnections. More specifically, a class of third-order CNNs with a nominal symmetric interconnection matrix is considered, and the Harmonic Balance (HB) method is exploited for addressing the possible existence of period-doubling bifurcations, and complex dynamics, for small perturbations of the nominal interconnections. The main result is that there are indeed parameter sets close to symmetry for which period-doubling bifurcations are predicted by the HB method. Moreover, the predictions are found to be reliable and accurate by means of computer simulations.

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