Yi Zhang, Tan K K, Lee T H
College of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China.
Neural Comput. 2003 Mar;15(3):639-62. doi: 10.1162/089976603321192112.
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.
多稳定性是神经网络中实现某些应用（如决策）所必需的一种特性，而单稳态网络在计算上可能具有局限性。本文着重分析一类具有不饱和分段线性传递函数的递归神经网络的多稳定性。它全面探讨了多稳态网络的三个基本特性：有界性、全局吸引性和完全收敛性。本文做出了以下贡献：推导了基于局部抑制的条件，以保证某些多稳态网络的有界性；建立了全局吸引性的条件，得到了全局吸引集的边界；使用新颖的类能量函数开发了网络的完全收敛条件，并通过仿真示例来说明由此发展的理论。
