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Cognitive Computation
Published in: Cognitive Computation 1/2024

17-10-2023

Stability Analysis of Quaternion-Valued Neutral Neural Networks with Generalized Activation Functions

Authors: Yanqiu Wu, Zhengwen Tu, Nina Dai, Liangwei Wang, Ning Hu, Tao Peng

Published in: Cognitive Computation | Issue 1/2024

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Abstract

Stability is a central issue in the study of dynamical systems, and quaternion-valued neural networks (QVNNs) perform well in handling the problem involving high-dimension date. The paper is dedicated to investigating the stability problem of QVNNs with neutral delay. In order to accurately estimate the derivative of Lyapunov functional, both reciprocally convex inequality and Wirtinger-based inequality are extended to the quaternion domain. And the direct quaternion method is used to analyze the quaternion-valued neutral neural networks (QVNNNs). Based on the generalized inequalities, the existence, uniqueness, and global stability criteria for QVNNS with several freedom matrices are derived. Concision and compact stability criteria of QVNNNs are established in the form of quaternion-valued LMIs, and the correctness of the theoretical results was verified through a numerical example.
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Literature
1.
Yang X, Li C, Song Q, Chen J, Huang J. Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw. 2018;105:88–103.CrossRef
2.
Wan A, Hong Q, Peng J, Wang M. Delay-independent criteria for exponential stability of generalized Cohen-Grossberg neural networks with discrete delays. Phys Lett A. 2006;353(2):151–7.CrossRef
3.
Zhang W, Yang S, Li C, Zhang W, Yang X. Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control. Neural Netw. 2018;104:93–103.CrossRef
4.
Li R, Cao J, Alsaedi A, Alsaadi F. Exponential and fixed-time synchronization of Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms. Appl Math Comput. 2017;313:37–51.MathSciNet
5.
Sheng Y, Huang T, Zeng Z. Exponential stabilization of fuzzy memristive neural networks with multiple time delays via intermittent control. IEEE Trans Syst Man Cybern: Syst. 2022;52(5):3092–101.CrossRef
6.
Xu C, Liao M, Li P, Guo Y, Liu Z. Bifurcation properties for fractional order delayed BAM neural networks. Cogn Comput. 2021;13(2):322–56.CrossRef
7.
Wei R, Cao J, Gorbachev S. Fixed-time control for memristor-based quaternion-valued neural networks with discontinuous activation functions. Cogn Comput. 2023;15(1):50–60.CrossRef
8.
Zhang W, Huang J. Stability analysis of stochastic delayed differential systems with state-dependent-delay impulses: application of neural networks. Cogn Comput. 2022;14(2):805–13.CrossRef
9.
Arena P, Baglio S, Fortuna L, Xibilia M. Chaotic time series prediction via quaternionic multilayer perceptrons. IEEE International Conference on Systems, Man and Cybernetics, Intelligent Systems for the 21st Century. 1995;1790–4.
10.
Kong G, Guo L. Stability analysis of delayed neural networks based on improved quadratic function condition. Neurocomputing. 2023;524:158–66.CrossRef
11.
Chen J, Park J, Xu S. Stability analysis for delayed neural networks with an improved general free-matrix-based integral inequality. IEEE Trans Neural Netw Learn Syst. 2019;31(2):675–84.MathSciNetCrossRef
12.
Zhang Y, Zhou L. Novel global polynomial stability criteria of impulsive complex-valued neural networks with multi-proportional delays. Neural Comput Appl. 2022;34:2913–24.CrossRef
13.
Song Q, Chen Y, Zhao Z, Liu Y, Alsaadi F. Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing. 2021;420:70–81.CrossRef
14.
Zhang W, Huang J. Stability analysis of stochastic delayed differential systems with state-dependent-delay impulses: application of neural networks. Cogn Comput. 2022;14(2):805–13.CrossRef
15.
Liu Y, Zhang D, Lu J, Cao J. Gobal μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inf Sci. 2016;360:273–88.CrossRef
16.
You X, Song Q, Liang J, Liu Y, Alsaadi F. Global μ-stability of quaternion-valued neural networks with mixed time-varying delays. Neurocomputing. 2018;290:12–25.CrossRef
17.
Wu A, Zeng Z, Zhu X, Zhang J. Exponential synchronization of memristor-based recurrent neural networks with time delays. Neurocomputing. 2011;74(17):3043–50.CrossRef
18.
Dhamala M, Jirsa V, Ding M. Enhancement of neural synchrony by time delay. Phys Rev Lett. 2004;92:074104.CrossRef
19.
Wu A, Zeng Z. Exponential stabilization of memristive neural networks with time delays. IEEE Trans Neural Netw Learn Syst. 2012;23(12):1919–29.CrossRef
20.
Yang X, Feng Y, Yiu K, Song Q, Alsaadi F. Synchronization of coupled neural networks with infinite-time distributed delays via quantized intermittent pinning control. Nonlinear Dyn. 2018;94(3):2289–303.CrossRef
21.
Chen J, Zhang X, Park J, Xu S. Improved stability criteria for delayed neural networks using a quadratic function negative-definiteness approach. IEEE Trans Neural Netw Learn Syst. 2020;33(3):1348–54.MathSciNetCrossRef
22.
Du F, Lu J. New results on finite-time stability of fractional-order Cohen-Grossberg neural networks with time delays. Asian J Control. 2022;438:107–20.MathSciNet
23.
Hu X, Wang L, Zeng Z, Zhu S, Hu J. Settling-time estimation for finite-time stabilization of fractional-order quaternion-valued fuzzy NNs. IEEE Trans Fuzzy Syst. 2022;30(12):5460–72.CrossRef
24.
Brayton R. Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type. Q Appl Math. 1966;24:215–24.MathSciNetCrossRef
25.
Zhang Z, Zhang X, Yu T. Global exponential stability of neutral-type Cohen-Grossberg neural networks with multiple time-varying neutral and discrete delays. Neurocomputing. 2022;490:124–31.CrossRef
26.
27.
Arik S. New criteria for stability of neutral-type neural networks with multiple time delays. IEEE Trans Neural Netw Learn Syst. 2019;31(5):1504–13.MathSciNetCrossRef
28.
Jian J, Wang B. Global Lagrange stability for neutral-type Cohen-Grossberg BAM neural networks with mixed time-varying delays. Math Comput Simul. 2015;116:1–25.MathSciNetCrossRef
29.
Xu D, Tan M. Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays. Nonlinear Dyn. 2017;89:819–32.CrossRef
30.
Tu Z, Cao J, Alsaedi A, Alsaadi F, Hayat T. Global Lagrange stability of complex-valued neural networks of neutral type with time-varying delays. Complexity. 2016;21:438–50.MathSciNetCrossRef
31.
Shu J, Xiong L, Wu T, Lu Z. Stability analysis of quaternion-valued neutral-type neural networks with time-varying delay. Mathematics. 2019;7(1):1–23.CrossRef
32.
Tu Z, Jian J, Wang B. Positive invariant and global exponential attractive sets of a class of neural networks with unbounded time-delays. Commun Nonlinear Sci Numer Simul. 2011;16:3738–45.MathSciNetCrossRef
33.
Liu Y, Wang Z, Liu X. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 2006;19(5):667–75.CrossRef
34.
Kwon O, Park M, Lee S, Park J, Cha E. Stability for neural networks with time-varying delays via some new approaches. IEEE Trans Neural Netw Learn Syst. 2013;24(2):181–93.CrossRef
35.
Zhang C, He Y, Jiang L, Wu M, Zeng H. Stability analysis of systems with time-varying delay via relaxed integral inequalities. Syst Control Lett. 2016;92:52–61.MathSciNetCrossRef
36.
Seuret A, Gouaisbaut F. Wirtinger-based integral inequality: application to time-delay systems. Automatica. 2013;49(9):2860–6.MathSciNetCrossRef
37.
Zhang C, He Y, Jiang L, Lin W, Wu M. Delay-dependent stability analysis of neural networks with time-varying delay: a generalized free-weighting-matrix approach. Appl Math Comput. 2017;294:102–20.MathSciNet
38.
39.
Tu Z, Cao J, Alsaedi A, Hayat T. Global dissipativity analysis for delayed quaternion-valued neural networks. Neural Netw. 2017;89:97–104.CrossRef
40.
Seuret A, Gouaisbaut F. Wirtinger-based integral inequality: application to time-delay systems. Automatica. 2013;49(9):2860–6.MathSciNetCrossRef
41.
Chen X, Li Z, Song Q, Hu J, Tan Y. Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Netw. 2017;91:55–65.CrossRef
42.
Boyd S, Ghaoui L, Feron E, Balakrishnan V. Linear matrix inequalities in system and control theory. Philadelphia: Society for industrial and applied mathematics; 1994.CrossRef
43.
Isokawa T, Kusakabe T, Matsui N, Peper F. Quaternion neural network and its application, Knowledge-Based Intelligent Information and Engineering Systems. 7th International Conference, KES. Oxford, UK, September 2003. Proceedings, Part II, Springer, Berlin. 2003;2003:318–24.
44.
Isokawa T, Matsui N, Nishimura H. Quaternionic neural networks: fundamental properties and applications, in Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters. Information Science Reference: Hershey, New York; 2009. p. 411–39.
45.
Wei R, Cao J. Fixed-time synchronization of quaternion-valued memristive neural networks with time delays. Neural Netw. 2019;113:1–10.CrossRef
46.
Wei R, Cao J. Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme. Cogn Neurodyn. 2019;13(5):489–502.CrossRef
47.
Tu Z, Cao J, Alsaedi A, Ahmad B. Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach. Nonlinear Anal: Model Control. 2018;23(3):361–79.MathSciNetCrossRef
Metadata
Title
Stability Analysis of Quaternion-Valued Neutral Neural Networks with Generalized Activation Functions
Authors
Yanqiu Wu
Zhengwen Tu
Nina Dai
Liangwei Wang
Ning Hu
Tao Peng
Publication date
17-10-2023
Publisher
Springer US
Published in
Cognitive Computation / Issue 1/2024
Print ISSN: 1866-9956
Electronic ISSN: 1866-9964
DOI
https://doi.org/10.1007/s12559-023-10212-w

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