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Continuous System
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Global dynamics in neural networks. III
Global dynamics in neural networks. III,10.1109/IJCNN.1991.155358,Fernanda Botelho,Max Garzon
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Global dynamics in neural networks. III
(
Citations: 3
)
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Fernanda Botelho
,
Max Garzon
A transform is introduced that maps discrete
neural network
dynamics to almost everywhere topologically conjugate dynamical systems on the unit interval. In many cases this correspondence gives rise to continuous conjugates, in which case the transform preserves entropy. The transform also allows transfer of many dynamical properties of continuous systems to a large class of infinite discrete neural networks. For instance, it is proved that the
network dynamics
of very simple classes of neural networks, even with highly symmetric weights and architectures, have chaotic regions of evolution (in the sense of existence of scrambled sets and configurations of arbitrarily large periods). These results raise the possibility of fully modeling parallel computability on realvalued dynamical systems by discrete neural nets
Conference:
International Symposium on Neural Networks  ISNN
, 1991
DOI:
10.1109/IJCNN.1991.155358
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Citation Context
(2)
...(For an interesting approach to computations on nets of unbounded size, see [
14
, 15, 18, 19].)...
Pekka Orponen
.
Neural Networks and Complexity Theory
...The main tool is a transform for neural networks regarded as dynamical systems on the Cantor sct [
8
,9,11] to dynamical systems on the euclidean unit ndimensional cubes...
...of the middle Cantor set of the unit interval in the real line R satisfying certain conditions (continuity and some finiteness conditions see [
8
,9,10]...
Fernanda Botelho
,
et al.
Global dynamics in neural networks. III
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Citations
(3)
Dynamic recurrent neural networks: a dynamical analysis
(
Citations: 28
)
Jeanphilippe Draye
,
Davor Pavisic
,
Guy Cheron
Journal:
IEEE Transactions on Systems, Man, and Cybernetics  TSMC
, vol. 26, no. 5, pp. 692706, 1996
Neural Networks and Complexity Theory
(
Citations: 13
)
Pekka Orponen
Conference:
Mathematical Foundations of Computer Science  MFCS
, pp. 5061, 1992
Global dynamics in neural networks. III
(
Citations: 3
)
Fernanda Botelho
,
Max Garzon
Conference:
International Symposium on Neural Networks  ISNN
, 1991