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Multistability Analysis for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions

elezy{at}nus.edu.sg, College of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China, and Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576

K. K. Tan

kktan{at}nus.edu.sg, Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576

T. H. Lee

eleleeth{at}nus.edu.sg, Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576

Multistability is a property necessary in neural networks in order to enable certain applications (e.g., decision making), where monostable networks can be computationally restrictive. This article focuses on the analysis of multistability for a class of recurrent neural networks with unsaturating piecewise linear transfer functions. It deals fully with the three basic properties of a multistable network: boundedness, global attractivity, and complete convergence. This article makes the following contributions: conditions based on local inhibition are derived that guarantee boundedness of some multistable networks, conditions are established for global attractivity, bounds on global attractive sets are obtained, complete convergence conditions for the network are developed using novel energy-like functions, and simulation examples are employed to illustrate the theory thus developed.

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