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Neural Computing and Applications

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18.04.2016 | Original Article

Multistability of complex-valued neural networks with distributed delays

verfasst von: Weiqiang Gong, Jinling Liang, Congjun Zhang

Erschienen in: Neural Computing and Applications | Sonderheft 1/2017

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Abstract

This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of \(9^n\) equilibrium points but also assure the local exponential stability for the \(4^n\) equilibrium points of them. Furthermore, the attraction basins of the \(4^n\) equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.

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Tanaka G, Aihara K (2009) Complex-valued multistate associative memory with nonlinear multilevel functions for gray-level image reconstruction. IEEE Trans Neural Netw 20(9):1463–1473CrossRef

Nitta T (2004) Orthogonality of decision boundaries in complex-valued neural networks. Neural Comput 16(1):73–97CrossRefMATH

Cha I, Kassam SA (1995) Channel equalization using adaptive complex radial basis function networks. IEEE J Sel Areas Commun 13(1):122–131CrossRef

Amin MF, Murase K (2009) Single-layered complex-valued neural network for real-valued classification problems. Neurocomputing 72(4–6):945–955CrossRef

Jankowski S, Lozowski A, Zurada JM (1996) Complex-valued multistate neural associative memory. IEEE Trans Neural Netw 7(6):1491–1496CrossRef

Zhou W, Zurada JM (2009) Discrete-time recurrent neural networks with complex-valued linear threshold neurons. IEEE Trans Circuits Syst II Exp Briefs 56(8):669–673CrossRef

Goh SL, Mandic DP (2004) A complex-valued RTRL algorithm for recurrent neural networks. Neural Comput 16(12):2699–2713CrossRefMATH

Lee DL (2001) Relaxation of the stability condition of the complex-valued neural networks. IEEE Trans Neural Netw 12(5):1260–1262CrossRef

Li C, Liao X, Yu J (2002) Complex-valued recurrent neural network with IIR neuron model: training and applications. Circuits Syst Signal Process 21(5):461–471MathSciNetCrossRefMATH

10.

Hirose A, Yoshida S (2013) Relationship between phase and amplitude generalization errors in complex- and real-valued feedforward neural networks. Neural Comput Appl 22(7–8):1357–1366CrossRef

11.

Hirose A (2006) Complex-Valued Neural Networks. Springer, BerlinCrossRefMATH

12.

Mostafa M, Teich WG, Lindner J (2014) Local stability analysis of discrete-time, continuous-state, complex-valued recurrent neural networks with inner state feedback. IEEE Trans Neural Netw Learn Syst 25(4):830–836CrossRef

13.

Rao VSH, Murthy GR (2008) Global dynamics of a class of complex valued neural networks. Int J Neural Syst 18(2):165–171CrossRef

14.

Lee D-L (2006) Improvements of complex-valued Hopfield associative memory by using generalized projection rules. IEEE Trans Neural Netw 17(5):1341–1347CrossRef

15.

Chakravarthy SV, Ghosh J (1996) A complex-valued associative memory for storing patterns as oscillatory states. Biol Cybern 75(3):229–238CrossRefMATH

16.

Bao G, Zeng Z (2013) Multistability of periodic delayed recurrent neural network with memristors. Neural Comput Appl 23(7):1963–1967CrossRef

17.

Cheng C-Y, Lin K-H, Shih C-W (2006) Multistability in recurrent neural networks. SIAM J Appl Math 66(4):1301–1320MathSciNetCrossRefMATH

18.

Huang G, Cao J (2010) Delay-dependent multistability in recurrent neural networks. Neural Netw 23(2):201–209CrossRef

19.

Nie X, Zheng WX (2015) Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. Neural Netw 65:65–79CrossRef

20.

Huang Y, Zhang H, Wang Z (2014) Multistability of complex-valued recurrent neural networks with real–imaginary-type activation functions. Appl Math Comput 229:187–200MathSciNetCrossRefMATH

21.

Rakkiyappan R, Velmurugan G, Cao J (2015) Multiple \(\mu\)-stability analysis of complex-valued neural networks with unbounded time-varying delays. Neurocomputing 149:594–607CrossRef

22.

Rudin W (1987) Real and Complex Analysis. McGraw-Hill, New YorkMATH

23.

Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865CrossRef

24.

Xu X, Zhang J, Shi J (2014) Exponential stability of complex-valued neural networks with mixed delays. Neurocomputing 128:483–490CrossRef

25.

Luo Y, Wei G, Liu Y, Ding X (2015) Reliable \(H_\infty\) state estimation for 2-D discrete systems with infinite distributed delays and incomplete observations. Int J Gen Syst 44(2):155–168MathSciNetCrossRefMATH

26.

Khajanchi S, Banerjee S (2014) Stability and bifurcation analysis of delay induced tumor immune interaction model. Appl Math Comput 248:652–671MathSciNetMATH

27.

Ali MS, Saravanakumar R, Zhu Q (2015) Less conservative delay-dependent \(H_\infty\) control of uncertain neural networks with discrete interval and distributed time-varying delays. Neurocomputing 166:84–95CrossRef

28.

Zeng X, Li C, Huang T, He X (2015) Stability analysis of complex-valued impulsive systems with time delay. Appl Math Comput 256:75–82MathSciNetMATH

29.

Fang T, Sun J (2014) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25(9):1709–1713CrossRef

30.

Song Q, Zhao Z, Liu Y (2015) Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168:1044–1050CrossRef

31.

Zhang Z, Lin C, Chen B (2014) Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(9):1704–1708CrossRef

32.

Zhou B, Song Q (2013) Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans Neural Netw Learn Syst 24(8):1227–1238CrossRef

33.

Song Q, Zhao Z, Liu Y (2015) Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159:96–104CrossRef

34.

Zhang Z, Yu S (2016) Global asymptotic stability for a class of complex-valued Cohen-Grossberg neural networks with time delays. Neurocomputing 171:1158–1166CrossRef

35.

Wang Z, Huang L (2016) Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173:2083–2089CrossRef

36.

Li Q, Shen B, Liang J, Shu H (2015) Event-triggered synchronization control for complex networks with uncertain inner coupling. Int J Gen Syst 44(2):212–225MathSciNetCrossRefMATH

37.

Perez-Cruz JH, Rubio JJ, Pacheco J, Soriano E (2014) State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks. Neural Comput Appl 25(3–4):693–701CrossRef

Titel: Multistability of complex-valued neural networks with distributed delays
verfasst von: Weiqiang Gong
Jinling Liang
Congjun Zhang
Publikationsdatum: 18.04.2016
Verlag: Springer London
Erschienen in: Neural Computing and Applications / Ausgabe Sonderheft 1/2017
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-016-2305-9

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