Asymptotic Analysis of Cyclic Transitions in the Discrete-Time Neural Networks with Antisymmetric and Circular Interconnection Weights
Summary :
Evaluation of cyclic transitions in the discrete-time neural networks with antisymmetric and circular interconnection weights has been derived in an asymptotic mathematical form. The type and the number of limit cycles generated by circular networks, in which each neuron is connected only to its nearest neurons, have been investigated through analytical method. The results show that the estimated numbers of state vectors generating n- or 2n-periodic limit cycles are an exponential function of (1.6)n for a large number of neuron, n. The sufficient conditions for state vectors to generate limit cycles of period n or 2n are also given.
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- IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.6 pp.1487-1490
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- 2004/06/01
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- Special Section LETTER (Special Section on Papers Selected from 2003 International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2003))
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Cheol-Young PARK, Koji NAKAJIMA, "Asymptotic Analysis of Cyclic Transitions in the Discrete-Time Neural Networks with Antisymmetric and Circular Interconnection Weights" in IEICE TRANSACTIONS on Fundamentals,
vol. E87-A, no. 6, pp. 1487-1490, June 2004, doi: .
Abstract: Evaluation of cyclic transitions in the discrete-time neural networks with antisymmetric and circular interconnection weights has been derived in an asymptotic mathematical form. The type and the number of limit cycles generated by circular networks, in which each neuron is connected only to its nearest neurons, have been investigated through analytical method. The results show that the estimated numbers of state vectors generating n- or 2n-periodic limit cycles are an exponential function of (1.6)n for a large number of neuron, n. The sufficient conditions for state vectors to generate limit cycles of period n or 2n are also given.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_6_1487/_p
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@ARTICLE{e87-a_6_1487,
author={Cheol-Young PARK, Koji NAKAJIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Asymptotic Analysis of Cyclic Transitions in the Discrete-Time Neural Networks with Antisymmetric and Circular Interconnection Weights},
year={2004},
volume={E87-A},
number={6},
pages={1487-1490},
abstract={Evaluation of cyclic transitions in the discrete-time neural networks with antisymmetric and circular interconnection weights has been derived in an asymptotic mathematical form. The type and the number of limit cycles generated by circular networks, in which each neuron is connected only to its nearest neurons, have been investigated through analytical method. The results show that the estimated numbers of state vectors generating n- or 2n-periodic limit cycles are an exponential function of (1.6)n for a large number of neuron, n. The sufficient conditions for state vectors to generate limit cycles of period n or 2n are also given.},
keywords={},
doi={},
ISSN={},
month={June},}
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TY - JOUR
TI - Asymptotic Analysis of Cyclic Transitions in the Discrete-Time Neural Networks with Antisymmetric and Circular Interconnection Weights
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1487
EP - 1490
AU - Cheol-Young PARK
AU - Koji NAKAJIMA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2004
AB - Evaluation of cyclic transitions in the discrete-time neural networks with antisymmetric and circular interconnection weights has been derived in an asymptotic mathematical form. The type and the number of limit cycles generated by circular networks, in which each neuron is connected only to its nearest neurons, have been investigated through analytical method. The results show that the estimated numbers of state vectors generating n- or 2n-periodic limit cycles are an exponential function of (1.6)n for a large number of neuron, n. The sufficient conditions for state vectors to generate limit cycles of period n or 2n are also given.
ER -
English
