EXISTENCE AND STABILITY OF ANTI PERIODIC SOLUTION FOR FCNNS WITH VARIABLE COEFFICIENTS IN THE LEAKAGE TERMS

TitleEXISTENCE AND STABILITY OF ANTI PERIODIC SOLUTION FOR FCNNS WITH VARIABLE COEFFICIENTS IN THE LEAKAGE TERMS
Publication TypeJournal Article
Year of Publication2019
AuthorsBAO HONGMEI
JournalDynamic Systems and Applications
Volume28
Issue2
Start Page275
Pagination14
Date Published02/2019
ISSN1056-2176
AMS Subject Classification34K13, 34K20, 92B20
Abstract

This paper is concerned with the problem of anti periodic solution for a class of fuzzy cellular neural networks (FCNNs) with variable coefficients in the leakage terms. Using contraction mapping and fixed point theorem and differential inequality, we obtain some sufficient conditions to guarantee the existence and exponential stability of the anti periodic solution for this model. These results complement previously known publications. Moreover a numerical example is given to show effectiveness of results obtained.
PDFhttps://acadsol.eu/dsa/articles/28/2/4.pdf
DOI10.12732/dsa.v28i2.4
Refereed DesignationRefereed
Full Text

[1] T. Yang, L. B. Yang, The global stability of fuzzy cellular neural networks. IEEE Trans. Circ. Syst. I, 43(1996), 880-883.
[2] T. Yang, L. B. Yang., C. W. Wu, L. O. Chua, Fuzzy cellular neural networks: theory. Proc IEEE Int Workshop Cellular Neural Networks Appl. (1996), 181186.
[3] K. Gopalsamy, Leakage delays in BAM. J Math Anal Appl, 325(2007), 1117-1132
[4] L. Peng, W. Wang, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms, Neurocomputing, bf 111(2013),27-33.
[5] T. Huang, Exponential stability of fuzzy cellular neural networks with distributed delay. Phys. Lett. A, 351(2006), 48-52.
[6] Y. Q. Liu, W. S. Tang, Exponential stability of fuzzy cellular neural networks with costant and time-varying delays.Phys. Lett. A, 323(2004), 224-233.
[7] Y. Q. Liu, W. S. Tang, Existence and exponential stability of periodic solution for BAM neural networks with periodic coefficients and delays. Neurocomputing, bf 69 (2006), 2152-2160. 
[8] K. Yuan, J. Cao, J. Deng, Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing, bf 69(2006), 1619-1627.
[9] Q. Zhang, R. Xiang, Global asymptotic stability of fuzzy cellular neural networks with time-varying delays. Phys. Lett. A, 372 (2008), 3971-3978.
[10] Q. Zhang, W. Luo, Global exponential stability of fuzzy BAM neural networks with time-varying delays. Chaos, Sol. Fract., 42(2009), 2239-2245.
[11] Q. Zhang, L. Yang, D. Liao, Existence and exponential stability of periodic solution for fuzzy BAM neural networks with periodic coefficient, Ukrainian Mathematical Journal, 63, No 12 (2012), 1900-1915.
[12] C. Ou, Anti-periodic solution for high-order Hopfield neural networks, Comput. Math. Appl., 56 (2008), 1838-1844.
[13] Y. K. Li, L. Yang, Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 3134-3140.
[14] Q. Zhou, Anti-periodic solutions for cellular neural networks with oscillating coefficients in leakage terms, Int. J. Mach. Learn. & Cyber., 2016, DOI 10.1007/s13042-016-0531-1
[15] G. Q. Peng, L.H. Huang, Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Nonlinear Anal. RWA, 10 (2009), 2434-2440.
[16] J.Y. Shao, An anti-periodic solution for a class of recurrent neural networks, J. Comput. Appl. Math., 228 (2009), 231-237.
[17] P. L. Shi, L.Z. Dong, Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses, Appl. Math. Comput., 216 (2010), 623-630.
[18] L. Pan, J. Cao, Anti-periodic solution for delayed cellular neural networks with impulsive effects, Nonlinear Analysis: Real World Applications, 12 (2011), 30143027.
[19] W. Wang, Anti-periodic solution for impulsive high-order Hopfield neural networks with time-varying delays in the leakage terms. Advances in Difference Equations,bf 2013 2013:273.
[20] Q. Zhang, L. Yang, J. Liu, Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen-Grossberge neural networks on time Scales, Math. Slovaca, 64 (2014), 119-138. 
[21] Y. Li, J. Shu, Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales, Commun Nonlinear Sci Numer Simulat.,16 (2011), 3326-3336.
[22] Z. Long, New results on anti-periodic solutions for SICNNs with oscillating coef?cients in leakage terms. Neurocomputing, 171(1) (2016), 503C509.
[23] H. Bao, On anti-periodic solutions for fuzzy BAM neural networks with constant delays on time scales, Dynamic Systems and Applications, 27, No. 3 (2018), 545-564.
[24] A. Jiang, Exponential Convergence for HCNNs with Oscillating Coefficients in Leakage Terms. Neural Process Lett., 43 (2016), 285-294.
[25] L. Berezansky, E. Braverman, On exponential stability of a linear delay differential equation with an oscillating coefficient. Appl Math Lett, bf 22(2009), 1833-1837.