Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10224192 | Applied Mathematics and Computation | 2019 | 27 Pages |
Abstract
This paper deals with the multistability problem of the quaternion-valued neural networks (QVNNs) with nonmonotonic piecewise nonlinear activation functions and unbounded time-varying delays. By virtue of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the QVNNs can be separated into four real-valued systems. By using the fixed point theorem and other analytical tools, some novel algebraic criteria are established to guarantee that the QVNNs can have 54n equilibrium points, 34n of which are locally μ-stable. Some criteria that guarantee the multiple exponential stability, multiple power stability, multiple log-stability, multiple log-log-stability are also derived as special cases. The obtained results reveal that the introduced QVNNs in this paper can have larger storage capacity than the complex-valued ones. Finally, one numerical example is presented to clarify the validity of the theoretical results.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Manchun Tan, Yunfeng Liu, Desheng Xu,