Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 26, Issue 11, Pages 2901-2913Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2015.2458978
Keywords
Discontinuous nonmonotonic piecewise linear activation functions; instability; multistability; neural networks
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Funding
- National Natural Science Foundation of China [61203300]
- Australian Research Council [DP120104986]
- 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 through Southeast University [3207012401]
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In this paper, we discuss the coexistence and dynamical behaviors of multiple equilibrium points for recurrent neural networks with a class of discontinuous nonmonotonic piecewise linear activation functions. It is proved that under some conditions, such n-neuron neural networks can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable, based on the contraction mapping theorem and the theory of strict diagonal dominance matrix. The investigation shows that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibrium points and more locally stable equilibrium points than the ones with continuous Mexican-hattype activation function or discontinuous two-level activation functions. An illustrative example with computer simulations is presented to verify the theoretical analysis.
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