Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions.
This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.
Yi
Zhang
Z
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China. zhangyi@uestc.edu.cn
Tan
Kok Kiong
KK
D016014:Linear Models; D016571:Neural Networks, Computer; D013997:Time Factors