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Synchronization schemes for coupled identical Yang-Yang type fuzzy cellular neural networks. (English) Zbl 1221.37227
Summary: We propose an adaptive procedure to the problem of synchronization for a class of coupled identical Yang-Yang type fuzzy cellular neural networks (YYFCNN) with time-varying delays. Based on the simple adaptive controller, a set of sufficient conditions are developed to guarantee the synchronization of the coupled YYFCNN with time-varying delays. The results are much different from previous ones. It is proved that two coupled identical YYFCNN with time-varying delays can achieve synchronization by enhancing the coupled strength dynamically. In addition, this kind of controller is simple to be implemented and it is fairly robust against the effect of weak noise in the given time series. The approaches are based on using the invariance principle of functional differential equations, constructing a general Lyapunov--Krasovskii functional and employing a linear matrix inequality (LMI). An illustrative example and its simulations show the feasibility of our results. Finally, an application is given to show how to apply the presented synchronization scheme of YYFCNN to secure communication.

37N35Dynamical systems in control
34K20Stability theory of functional-differential equations
37D45Strange attractors, chaotic dynamics
92B20General theory of neural networks (mathematical biology)
93C42Fuzzy control systems
Full Text: DOI
[1] Chua, L. O.; Yang, L.: Cellular neural networks: applications, IEEE trans circ syst 35, 1273-1290 (1988)
[2] Hopfield, J. J.: Neurons with graded response have collective computational properties like those of two-state neurons, Proc natl acad sci 81, 3088-3092 (1984)
[3] Cao, J.: Global stability conditions for delayed cnns, IEEE trans circ syst I 48, 1330-1333 (2001) · Zbl 1006.34070 · doi:10.1109/81.964422
[4] Cao, J.; Wang, J.: Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE trans circ syst I 52, 920-931 (2005)
[5] Xia, Y. H.; Cao, J.; Lin, M.: New results on the existence and uniqueness of almost periodic solutions for BAM neural networks with continuously distributed delays, Chaos, solitons & fractals 31, 928-936 (2007) · Zbl 1137.68052 · doi:10.1016/j.chaos.2005.10.043
[6] Xia, Y. H.; Cao, J.; Huang, Z.: Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos, solitons & fractals 34, 1599-1607 (2007) · Zbl 1152.34343
[7] Xia, Y. H.; Cao, J.; Cheng, S. S.: Global exponential stability of delayed cellular neural networks with impulses, Neurocomputing 70, 2495-2501 (2007)
[8] Yang, T.; Yang, L. B.: The global stability of fuzzy cellular neural networks, IEEE trans circ syst I 43, 880-883 (1996)
[9] Yang, T.; Yang, L. B.: Application of fuzzy cellular neural network to morphological grey-scale reconstruction, Int circ theory appl 25, 153C165 (1997) · Zbl 0886.68129 · doi:10.1002/(SICI)1097-007X(199705/06)25:3<153::AID-CTA959>3.0.CO;2-L
[10] Yang, T.; Yang, L. B.: Application of fuzzy cellular neural networks to Euclidean distance transformation, IEEE trans circ syst I 44, 242-246 (1997)
[11] Liu, Y.; Tang, W.: Exponential stability of fuzzy neural networks with constant and time-varying delays, Phys lett A 323, 224-233 (2004) · Zbl 1118.81400 · doi:10.1016/j.physleta.2004.01.064
[12] Yuan, K.; Cao, J.; Deng, J.: Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays, Neurocomputing 69, 1619-1627 (2006)
[13] Song, Q.; Cao, J.: Impulsive effects on stability of fuzzy Cohen -- Grossberg neural networks with time-varying delays, IEEE trans syst man cybernet B 37, 733-741 (2007)
[14] Zou, F.; Nossek, J. A.: Bifurcation and chaos in cellular neural networks, IEEE trans circ syst I 40, 166-173 (1993) · Zbl 0782.92003 · doi:10.1109/81.222797
[15] Lu, H. T.: Chaotic attractors in delayed neural networks, Phys lett A 298, 109-116 (2002) · Zbl 0995.92004 · doi:10.1016/S0375-9601(02)00538-8
[16] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys rev lett 64, 821-824 (1990) · Zbl 0938.37019
[17] Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys rev lett 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[18] Cao J, Lu J. Adaptive synchronization of neural networks with or without time-varying delays. Chaos 2006;16, art. no. 013133. · Zbl 1144.37331 · doi:10.1063/1.2178448
[19] Huang, X.; Cao, J.: Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme, Nonlinearity 19, 2797-2811 (2006) · Zbl 1111.37022 · doi:10.1088/0951-7715/19/12/004
[20] Sun, Y.; Cao, J.: Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation, Phys lett A 364, 277-285 (2007) · Zbl 1203.93110 · doi:10.1016/j.physleta.2006.12.019
[21] Chen, G.; Zhou, J.; Liu, Z.: Global synchronization of coupled delayed neural networks and applications to chaotic CNN model, Int J bifurc chaos 14, 2229-2240 (2004) · Zbl 1077.37506 · doi:10.1142/S0218127404010655
[22] Zhou, J.; Chen, T.: Synchronization in general complex delayed dynamical networks, IEEE trans circ syst I 53, 733-744 (2006)
[23] Wu, C. W.: Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems, Phys lett A 319, 495-503 (2003) · Zbl 1029.37018 · doi:10.1016/j.physleta.2003.10.063
[24] Hale, J. K.: Theory of functional differential equations, (1977) · Zbl 0352.34001
[25] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994) · Zbl 0816.93004
[26] Wu, H.; Xue, X.: Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses, Appl math model 32, 2347-2359 (2008) · Zbl 1156.34333 · doi:10.1016/j.apm.2007.09.002
[27] Wu, H.; Sun, J.; Zhong, X.: Analysis of dynamical behaviour for delayed neural networks with inverse Lipschitzian neuron activations and impulses, Int J innovative comput inform control 4, 705-715 (2008)
[28] Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach, IEE proc contr theory appl 151, 125-129 (2004)
[29] Singh, V.: Global robust stability of delayed neural networks: an LMI approach, IEEE trans circ syst II 52, 33-36 (2005)
[30] Singh, V.: On global robust stability of interval Hopfield neural networks with delay, Chaos, solitons & fractals 33, 1183-1188 (2007) · Zbl 1151.34333
[31] Huang, Z. T.; Yang, Q. G.; Luo, X.: Exponential stability of impulsive neural networks with time-varying delays, Chaos, solitons & fractals 35, 770-780 (2008) · Zbl 1139.93353
[32] Ding, W.: Synchronization of fuzzy cellular neural networks based on adaptive control, Phys lett A 372, 4674-4681 (2008) · Zbl 1221.94094 · doi:10.1016/j.physleta.2008.04.053
[33] Arik, S.; Tavsanoglu, V.: Equilibrium analysis of delayed cnn’s, IEEE trans circ syst I 45, 168-171 (1998) · Zbl 0917.68223
[34] Arik, S.: Global asymptotic stability of a larger class of neural networks with constant time delays, Phys lett A 311, 504-511 (2003) · Zbl 1098.92501 · doi:10.1016/S0375-9601(03)00569-3