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Title: Matrix criterion for dynamic analysis in discrete neural networks with multiple delays
Authors: Tsang, ECC
Qiu, SS
Yeung, DS
Keywords: Hopfield neural nets
Limit cycles
Matrix algebra
Discrete Hopfield neural network
Fixed points
Limit cycle
Matrix inequality
Multiple delays
Issue Date: 2002
Publisher: IEEE
Source: 2002 International Conference on Machine Learning and Cybernetics, 2002 : proceedings : 4-5 November 2002, v. 4, p. 2245-2250 How to cite?
Abstract: The dynamics of a discrete Hopfield neural network with multiple delays (HNNMDs) is studied by using a matrix inequality which is shown to be equivalent to the state transition equation of the HNNMDs network. Earlier work (2000) on discrete Hopfield neural networks showed that a parallel or serial mode of operation always leads to a limit cycle of period one or two for a skew or symmetric matrix, but they did not give an arbitrary weight matrix on how an updating operation might be needed to reach such a cycle. In this paper we present the existence conditions of limit cycles using matrix criteria in the HNNMDs network. For a network with an arbitrary weight matrix, the necessary and sufficient conditions for the existence of a limit cycle of period 1 and r are provided. The conditions for the existence of a special limit cycle of period 1 and 2 are also found. These results provide the foundation for many applications. A HNNMDs is said to have no stable state (fixed point) if it has a limit cycle of period 2 or more, which is stated in Theorem 5. A computer simulation demonstrates that the theoretical analysis in Theorem 5 is correct.
ISBN: 0-7803-7508-4
DOI: 10.1109/ICMLC.2002.1175439
Appears in Collections:Conference Paper

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