Quantitative properties of the equilibrium point of an associative memory neural network

Lisheng Wang; Zheng Tan

doi:10.1117/12.342908

22 March 1999 Quantitative properties of the equilibrium point of an associative memory neural network

Lisheng Wang, Zheng Tan

Proceedings Volume 3722, Applications and Science of Computational Intelligence II; (1999) https://doi.org/10.1117/12.342908
Event: AeroSense '99, 1999, Orlando, FL, United States

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.

Citation Download Citation

Lisheng Wang and Zheng Tan "Quantitative properties of the equilibrium point of an associative memory neural network", Proc. SPIE 3722, Applications and Science of Computational Intelligence II, (22 March 1999); https://doi.org/10.1117/12.342908

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