期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 46, 期 3, 页码 679-693出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2015.2413212
关键词
Competitive neural networks; discontinuous nonmonotonic piecewise linear activation functions; instability; multistability
类别
资金
- Australian Research Council [DP120104986]
- National Natural Science Foundation of China [61203300]
- Specialized Research Fund for the Doctoral Program of Higher Education [20120092120029]
- Natural Science Foundation of Jiangsu Province of China [BK2012319]
- China Post-Doctoral Science Foundation [2012M511177]
- Innovation Foundation of Southeast University [3207012401]
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n-neuron competitive neural networks can have 5n equilibria, among which 3n equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3n locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
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