Stability analysis of multiple equilibria for recurrent neural networks

Authors:
Yujiao Huang;Huaguang Zhang;Zhanshan Wang;Mo Zhao
Affiliations:
School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China;School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China;School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China;School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China
Venue:
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
Year:
2012

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Abstract

This paper is concerned with the dynamical stability analysis of multiple equilibrium points in recurrent neural networks with piecewise linear nondecreasing activation functions. By a geometrical observation, conditions are obtained to ensure that n-dimensional recurrent neural networks with r-stair piecewise linear nondecreasing activation functions can have (2r+1)n equilibrium points. Positively invariant regions for the solution flows generated by the system are established. It is shown that this system can have (r+1)n locally exponentially stable equilibrium points located in invariant regions. Moreover, the result is presented that there exist (2r+1)n−(r+1)n unstable equilibrium points for the system. Finally, an example is given to illustrate the effectiveness of the results.