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Proceedings Paper

Quantitative properties of the equilibrium point of an associative memory neural network
Author(s): Lisheng Wang; Zheng Tan
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Paper Abstract

The stable properties of equilibrium point are the most important properties of associative memory neural network, which include local stability, domain of absorb and convergent rate. Because associative memory neural network has a lot of equilibrium points, and different equilibrium point has different stable properties, so it is an interesting and important research problem to reveal the quantitative relation between equilibrium point and its stable properties. In the paper, the following three results are proved: (1) the equilibrium point X* is locally exponentially stable if and only if the real parts of all eigenvalues of derivative (matrix) of network at X* are less than zero; (2) the fastest convergent speed of trajectory of equilibrium point X* is equal to the maximum of real parts of all eigenvalues of derivative (matrix) of network at X*; (3) the domain of absorb of equilibrium point X* is determined by the change rate of output function in the local neighborhood of X*, and its estimate can be obtained by the computation of a local characteristic function of X* defined in the paper. From all these results, people can see that the stable properties of a given equilibrium point of associative memory neural network are uniquely determined by the equilibrium point itself. So as a matter of fact, equilibrium point can be thought as an information point containing the important information about its stability.

Paper Details

Date Published: 22 March 1999
PDF: 8 pages
Proc. SPIE 3722, Applications and Science of Computational Intelligence II, (22 March 1999); doi: 10.1117/12.342908
Show Author Affiliations
Lisheng Wang, Xi'an JiaoTong Univ. (China)
Zheng Tan, Xi'an JiaoTong Univ. (China)


Published in SPIE Proceedings Vol. 3722:
Applications and Science of Computational Intelligence II
Kevin L. Priddy; Paul E. Keller; David B. Fogel; James C. Bezdek, Editor(s)

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