Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 341, Issue -, Pages 229-255Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2018.08.033
Keywords
Quaternion-valued neural networks; Multistability; mu-stability; Nonmonotonic piecewise nonlinear activation functions; Unbounded time delays
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Funding
- National Natural Science Foundation of China [61572233, 11471083]
- Science and Technology Program of Guangzhou, China [201707010404]
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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 5(4n) equilibrium points, 3(4n) of which are locally mu-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. (c) 2018 Elsevier Inc. All rights reserved.
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