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.
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Huang, Y., Zhang, H., Wang, Z., Zhao, M. (2012). Stability Analysis of Multiple Equilibria for Recurrent Neural Networks. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_23
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DOI: https://doi.org/10.1007/978-3-642-31346-2_23
Publisher Name: Springer, Berlin, Heidelberg
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