×

Synchronization of coupled reaction-diffusion neural networks with hybrid coupling via aperiodically intermittent pinning control. (English) Zbl 1373.93025

Summary: This paper investigates the complete synchronization for linearly coupled neural networks with time-varying delays and reaction-diffusion terms by using the aperiodically intermittent pinning control. The coupling matrix for the network can be asymmetric. Compared with state coupling in the synchronization literature, we design a novel distributed coupling protocol by using the reaction-diffusion coupling: spatial coupling, which can accelerate the synchronization process. This can be regarded as the main difference between this paper and previous works. Using the Lyapunov function and theories in the aperiodically intermittent control, we present some criteria for the complete synchronization with a static coupling strength. In this case, there is no constraint on the bound of time-varying delays, so it can be larger than the length of control span. On the other hand, we also consider the network with an adaptive coupling strength. In this case, the infimum of the control time span should be larger than the upper bound of time delay. Numerical simulations are given to show correctness of obtained results.

MSC:

93A14 Decentralized systems
92B20 Neural networks for/in biological studies, artificial life and related topics
35K57 Reaction-diffusion equations
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Huang, D. S., Radial basis probabilistic neural networks: model and application, Int. J. Pattern Recognit. Artif. Intell., 13, 7, 1083-1101 (1999)
[2] Huang, D. S., A constructive approach for finding arbitrary roots of polynomials by neural networks, IEEE Trans. Neural Netw., 15, 2, 477-491 (2004)
[3] Turing, A. M., The chemical basis of morphogenesis, Philos. Trans. R. S. Lond. Ser. B, 237, 37-72 (1952) · Zbl 1403.92034
[4] Alonso, S.; John, K.; Bar, M., Complex wave patterns in an effective reaction-diffusion model for chemical reactions in microemulsions, J. Chem. Phys., 134, 9, 094117 (2011)
[5] Liang, J. L.; Cao, J. D., Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays, Phys. Lett. A, 314, 5-6, 434-442 (2003) · Zbl 1052.82023
[6] Lu, J. G., Robust global exponential stability for interval reaction-diffusion Hopfield neural networks with distributed delays, IEEE Trans. Circuits Syst. II, 54, 12, 1115-1119 (2007)
[7] Lu, J. G., Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, Chaos Solitons Fractals, 35, 1, 116-125 (2008) · Zbl 1134.35066
[8] Qiu, J. L., Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms, Neurocomputing, 70, 4-6, 1102-1108 (2007)
[9] Chen, Z.; Zhao, D. H., Stabilization effect of diffusion in delayed neural networks systems with Dirichlet boundary conditions, J. Frankl. Inst., 348, 10, 2884-2897 (2011) · Zbl 1254.93141
[10] Chen, Z.; Fu, X. L.; Zhao, D. H., Anti-periodic mild attractor of delayed Hopfield neural networks systems with reaction-diffusion terms, Neurocomputing, 99, 372-380 (2013)
[11] Wu, C. W.; Chua, L. O., Synchronization in an array of linearly coupled dynamical-systems, IEEE Trans. Circuits Syst. I, 42, 8, 430-447 (1995) · Zbl 0867.93042
[12] Lu, W. L.; Chen, T. P., New approach to synchronization analysis of linearly coupled ordinary differential systems, Phys. D, 213, 2, 214-230 (2006) · Zbl 1105.34031
[13] Chen, T. P.; Liu, X. W.; Lu, W. L., Pinning complex networks by a single controller, IEEE Trans. Circuits Syst. I, 54, 6, 1317-1326 (2007) · Zbl 1374.93297
[14] Liu, X. Y.; Cao, J. D.; Jiang, N.; Hao, G. S.; Wang, S. M., Finite-time consensus of second-order multi-agent systems via auxiliary system approach, J. Frankl. Inst., 353, 7, 1479-1493 (2016) · Zbl 1336.93019
[15] Wan, Y.; Cao, J. D., Distributed robust stabilization of linear multi-agent systems with intermittent control, J. Frankl. Inst., 352, 10, 4515-4527 (2015) · Zbl 1395.93471
[16] Li, H. J.; Su, H. Y., Distributed consensus of multi-agent systems with nonlinear dynamics via adaptive intermittent control, J. Frankl. Inst., 352, 10, 4546-4564 (2015) · Zbl 1395.93015
[17] Liu, M.; Jiang, H. J.; Hu, C., Synchronization of hybrid-coupled delayed dynamical networks via aperiodically intermittent pinning control, J. Frankl. Inst., 353, 12, 2722-2742 (2016) · Zbl 1347.93213
[18] Ambrosio, B.; Aziz-Alaoui, M. A., Synchronization and control of coupled reaction-diffusion systems of the Fitzhugh-Nagumo type, Comput. Math. Appl., 64, 934-943 (2012) · Zbl 1356.93039
[19] Kao, Y. G.; Wang, C. H.; Karimi, H. R.; Bi, R., Global stability of coupled Markovian switching reaction-diffusion systems on networks, Nonlinear Anal. Hybrid Syst., 13, 61-73 (2014) · Zbl 1292.93140
[20] Wang, Y. Y.; Cao, J. D., Synchronization of a class of delayed neural networks with reaction-diffusion terms, Phys. Lett. A, 369, 3, 201-211 (2007)
[21] Sheng, L.; Yang, H. Z.; Lou, X. Y., Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms, Chaos Solitons Fractals, 40, 2, 930-939 (2009) · Zbl 1197.35148
[22] Wang, K.; Teng, Z. D.; Jiang, H. J., Adaptive synchronization in an array of linearly coupled neural networks with reaction-diffusion terms and time delays, Commun. Nonlinear Sci. Numer. Simul., 17, 10, 3866-3875 (2012) · Zbl 1253.92004
[23] Wang, J. L.; Wu, H. N.; Guo, L., Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms, IEEE Trans. Neural Netw. Learn. Syst., 25, 2, 429-440 (2014)
[24] Liu, X. W., Synchronization of linearly coupled neural networks with reaction-diffusion terms and unbounded time delays, Neurocomputing, 73, 13-15, 2681-2688 (2010)
[25] Yu, F.; Jiang, H. J., Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms, Neurocomputing, 74, 4, 509-515 (2011)
[26] Gan, Q. T., Adaptive synchronization of stochastic neural networks with mixed time delays and reaction-diffusion terms, Nonlinear Dyn., 69, 4, 2207-2219 (2012) · Zbl 1263.35143
[27] Shi, G. D.; Ma, Q., Synchronization of stochastic Markovian jump neural networks with reaction-diffusion terms, Neurocomputing, 77, 1, 275-280 (2012)
[28] Wu, K. N.; Chen, B. S., Synchronization of partial differential systems via diffusion coupling, IEEE Trans. Circuits Syst. I, 59, 11, 2655-2668 (2012) · Zbl 1468.93085
[29] Wang, J. L.; Wu, H. N., Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling, IEEE Trans. Cybern., 44, 8, 1350-1361 (2014)
[30] Xu, B. B.; Huang, Y. L.; Wang, J. L.; Wei, P. C.; Ren, S. Y., Passivity of linearly coupled neural networks with reaction-diffusion terms and switching topology, J. Frankl. Inst., 353, 8, 1882-1898 (2016) · Zbl 1347.93231
[31] Wang, J. L.; Wu, H. N.; Huang, T. W.; Ren, S. Y., Pinning control strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms, IEEE Trans. Neural Netw. Learn. Syst., 27, 4, 749-761 (2016)
[32] Hu, C.; Jiang, H. J.; Teng, Z. D., Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms, IEEE Trans. Neural Netw., 21, 1, 67-81 (2010)
[33] Rakkiyappan, R.; Dharani, S.; Zhu, Q. X., Synchronization of reaction-diffusion neural networks with time-varying delays via stochastic sampled-data controller, Nonlinear Dyn., 79, 1, 485-500 (2015) · Zbl 1331.92018
[34] Rakkiyappan, R.; Chandrasekar, A.; Park, J. H.; Kwon, O. M., Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control, Nonlinear Anal. Hybrid Syst., 14, 16-37 (2014) · Zbl 1292.93109
[35] Wang, J. Y.; Zhang, H. G.; Wang, Z. S., Sampled-data synchronization for complex networks based on discontinuous LKF and mixed convex combination, J. Frankl. Inst., 352, 11, 4741-4757 (2015) · Zbl 1395.93360
[36] Hu, C.; Yu, J.; Jiang, H. J.; Teng, Z. D., Exponential synchronization for reaction-diffusion networks with mixed delays in terms of \(p\)-norm via intermittent driving, Neural Netw., 31, 1-11 (2012) · Zbl 1245.93122
[37] Gan, Q. T., Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control, Neural Netw., 31, 12-21 (2012) · Zbl 1245.93125
[38] Mei, J.; Jiang, M. H.; Wang, B.; Liu, Q.; Xu, W. M.; Liao, T., Exponential \(p\)-synchronization of non-autonomous Cohen-Grossberg neural networks with reaction-diffusion terms via periodically intermittent control, Neural Process. Lett., 40, 2, 103-126 (2014)
[39] Gan, Q. T.; Lv, T. S.; Fu, Z. H., Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control, Chaos, 26, 043113 (2016) · Zbl 1361.34060
[40] Liu, X. W.; Chen, T. P., Cluster synchronization in directed networks via intermittent pinning control, IEEE Trans. Neural Netw., 22, 7, 1009-1020 (2011)
[41] Liu, X. W.; Chen, T. P., Synchronization of complex networks via aperiodically intermittent pinning control, IEEE Trans. Autom. Control, 60, 12, 3316-3321 (2015) · Zbl 1360.93359
[42] Liu, X. W.; Chen, T. P., Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control, IEEE Trans. Neural Netw. Learn. Syst., 26, 1, 113-126 (2015)
[43] Liu, X. W.; Chen, T. P., Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control, IEEE Trans. Neural Netw. Learn. Syst., 26, 10, 2396-2407 (2015)
[44] Wei, Y. L.; Qiu, J. B.; Karimi, H. R.; Wang, M., A new design of \(h_∞\) filtering for continuous-time Markovian jump systems with time-varying delay and partially accessible mode information, Signal Process, 93, 9, 2392-2407 (2013)
[45] Wei, Y. L.; Qiu, J. B.; Karimi, H. R.; Wang, M., Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information, Inf. Sci., 269, 316-331 (2014) · Zbl 1339.93111
[46] Wei, Y. L.; Qiu, J. B.; Karimi, H. R.; Wang, M., New results on \(h_∞\) dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information, Optim. Control Appl. Methods, 35, 6, 656-675 (2014) · Zbl 1305.93184
[47] Wei, Y. L.; Qiu, J. B.; Karimi, H. R.; Wang, M., Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information, Multidimens. Syst. Signal Process, 26, 3, 575-597 (2015) · Zbl 1349.62381
[48] Liu, X. W.; Chen, G. J., Cluster synchronization for nonidentical reaction-diffusion neural networks with hybrid coupling, Proceedings of the Third International Conference on Systems and Informatics, 1-6 (2016), Shanghai
[49] Liu, X. W.; Wu, J. L., Exponential synchronization for delayed reaction-diffusion neural networks through hybrid coupling, Proceedings of the Third International Conference on Systems and Informatics, 19-23 (2016), Shanghai
[50] Liu, X. W.; Wei, Y. T., Finite-time cluster synchronization of nonlinearly coupled reaction-diffusion neural networks via spatial coupling and control, Proceedings of the Third International Conference on Systems and Informatics, 24-29 (2016), Shanghai
[51] Chou, H. G.; Chuang, C. F.; Wang, W. J.; Lin, J. C., A fuzzy-model-based chaotic synchronization and its implementation on a secure communication system, IEEE Trans. Inf. Forensics Secur., 8, 12, 2177-2185 (2013)
[52] Huang, C.; Ho, D. W.C.; Lu, J. Q.; Kurths, J., Pinning synchronization in T-S fuzzy complex networks with partial and discrete-time couplings, IEEE Trans. Fuzzy Syst., 23, 4, 1274-1285 (2015)
[53] Wei, Y. L.; Qiu, J. B.; Karimi, H. R., Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults, IEEE Trans. Circuits Syst. I, 64, 1, 170-181 (2017)
[54] Kammler, D. W., A First Course in Fourier Analysis (2007), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1144.42001
[55] X. Zhang, Y.Y. Han, L.G. Wu, Y.T. Wang, State estimation for delayed genetic regulatory networks with reaction-diffusion terms, IEEE Trans. Neural Netw. Learn. Syst., https://doi.org/10.1109/TNNLS.2016.2618899.; X. Zhang, Y.Y. Han, L.G. Wu, Y.T. Wang, State estimation for delayed genetic regulatory networks with reaction-diffusion terms, IEEE Trans. Neural Netw. Learn. Syst., https://doi.org/10.1109/TNNLS.2016.2618899.
[56] Liu, X. W.; Li, S. H., Cluster synchronization for linearly coupled nonidentical systems with delays via aperiodically intermittent pinning control, IEEE Access, 5, 4179-4189 (2017)
[57] X.W. Liu, Z. Chen, L.J. Zhou, Synchronization of linearly coupled reaction-diffusion neural networks with hybrid coupling and time-varying delays via aperiodically intermittent pinning control, (arXiv:1604.03379; X.W. Liu, Z. Chen, L.J. Zhou, Synchronization of linearly coupled reaction-diffusion neural networks with hybrid coupling and time-varying delays via aperiodically intermittent pinning control, (arXiv:1604.03379 · Zbl 1373.93025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.