Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Mixed Time Delays
Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Mixed Time Delays
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DOI：
10.1109/tsmc.2015.2461191
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Peng Liu;Z. Zeng;Jun Wang
中科院分区：
文献类型：
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作者：
Peng Liu;Z. Zeng;Jun Wang
本文给出了一类具有非单调激活函数和混合时滞的递归神经网络多稳定性分析的新理论结果。利用激活函数的几何性质和非奇异M-矩阵的代数性质，得到了通过状态空间划分确定3n个平衡点的存在和2n个平衡点的指数稳定性的几个充分条件。与已有结果相比，本文条件的计算量大大减少了一阶线性矩阵不等式。此外，还估计了这些指数稳定平衡点的吸引盆。结果表明，这2n个平衡点的吸引盆可以比它们原来划分的子空间大。用典型的非单调激活函数给出了三个数值算例，验证了理论结果的有效性和特点。
This paper presents new theoretical results on the multistability analysis of a class of recurrent neural networks with nonmonotonic activation functions and mixed time delays. Several sufficient conditions are derived for ascertaining the existence of 3n equilibrium points and the exponential stability of 2n equilibrium points via state space partition by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. Compared with existing results, the conditions herein are much more computable with one order less linear matrix inequalities. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of the 2n equilibrium points can be larger than their originally partitioned subspaces. Three numerical examples are elaborated with typical nonmonotonic activation functions to substantiate the efficacy and characteristics of the theoretical results.