期刊
NEUROCOMPUTING
卷 216, 期 -, 页码 135-142出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.neucom.2016.07.032
关键词
Multistability; Nonincreasing activation function; Nondecreasing activation function; Recurrent neural networks
资金
- Key Program of National Natural Science Foundation of China [61134012]
- Doctoral Program of Higher Education of China [20130142130012]
- Science and Technology Support Program of Hubei Province [2015BHE013]
- Program for Science and Technology in Wuhan of China [2014010101010004]
In this paper, we are concerned with a class of recurrent neural networks (RNNs) with nonincreasing activation function. First, based on the fixed point theorem, it is shown that under some conditions, such an n dimensional neural network with nondecreasing activation function can have at least (4k + 3)(n) equilibrium points. Then, it proves that there is only (4k + 3)(n) equilibria under some conditions, among which (2k + 2)(n) equilibria are locally stable. Besides, by analysis and study of RNNs with nondecreasing activation function, we can also obtain the same number of equilibria for RNNs with nonincreasing activation function. Finally, two simulation examples are given to show effectiveness of the obtained results. (C) 2016 Elsevier B.V. All rights reserved.
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