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.
KEYWORDS: Sensors, Data processing, Image processing, 3D image processing, Visualization, Data storage, Edge detection, Algorithm development, Algorithms, Data visualization
In data visualization, an efficient method for decreasing computation and storage is to extract feature region from massive data set and process (visualize, store or transmit) it solely. For this reason, in this paper, we will develop some algorithms for extracting region containing feature and for detecting edge points from 3D mesh data.
In this paper, a characteristic function is defined and used to quantitatively characterize exponential stability of nonlinear continuous neural network. By utilizing the function, we address many important aspects of network, including global and local exponential stability; the estimates of the domain of attraction of stable equilibrium point; the estimates of convergent rate of the network trajectories. A sufficient and necessary condition for network to be locally exponentially stable is obtained. Our method is simple and practical, and our results generalize those in 1-3.
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