Abstract
In this chapter, we are concerned with exponential stability analysis for neural networks with fuzzy logical BAM and Markovian jump and synchronization control problem of stochastically coupled neural networks.
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References
P.B. Ali, M. Syed, Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays. Math. Comput. Model. 53(1), 151–160 (2011)
S. Arik, V. Tavsanoglu, Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68, 161–176 (2005)
P. Balasubramanian, R. Rakkiyappan, R. Sathy, Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters. Expert Syst. Appl. 38(1), 121–130 (2011)
R. Belohlavek, Fuzzy logical bidirectional associative memory. Inf. Sci. 128(1), 91–103 (2000)
J. Cao, P. Li, W. Wang, Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys. Lett. A 353(4), 318–325 (2006)
J. Cao, X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Phys. D 212(1), 54–65 (2005)
J. Cao, Z. Wang, Y. Sun, Synchronization in an array of linearly stochastically coupled networks with time-delays. Phys. A: Stat. Mech. Appl. 385(2), 718–728 (2007)
G.R. Chen, J. Zhou, Z.R. Liu, Global synchronization of coupled delayed neural networks and applications to chaotic CNN model. Int. J. Bifurc. Chaos 14(7), 2229–2240 (2004)
M. Chen, D. Zhou, Synchronization in uncertain complex networks. Chaos: an interdisciplinary. J. Nonlinear Sci. 16(1), 013101 (2006)
B. Kosko, Adaptive bi-directional associative memories. Appl. Opt. 26(23), 4947–4960 (1987)
B. Kosko, Bi-directional associative memories. IEEE Trans. Syst., Man Cybern 18(1), 49–60 (1988)
B. Kosko, Neural Networks and Fuzzy Systems—A Dynamical System Approach to Machine Intelligence (Prentice-Hall, Englewood Cliffs, 1992)
C. Li, S. Li, X. Liao, J. Yu, Synchronization in coupled map lattices with small-world delayed interactions. Phys. A 335(3), 365–370 (2004)
C.G. Li, G.R. Chen, Synchronization in general complex dynamical networks with coupling delays. Phys. A 343, 263–278 (2004)
P. Li, J. Cao, Z. Wang, Robust impulsive synchronization of coupled delayed neural networks with uncertainties. Phys. A 373, 261–272 (2007)
Z. Li, G. Chen, Robust adaptive synchronization of uncertain dynamical networks. Phys. Lett. A 324(2), 166–178 (2004)
W. Lin, G. Chen, Using white noise to enhance synchronization of coupled chaotic systems. Chaos 16(1), 013133–013134 (2006)
B. Liu, X.Z. Liu, G.R. Chen, Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuits Syst. I 52(7), 1431–1441 (2005)
B. Liu, P. Shi, Delay-range-dependent stability for fuzzy BAM neural networks with time-varying delays. Phys. Lett. A 373(21), 1830–1838 (2009)
X. Lou, B. Cui, Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays. Fuzzy Sets Syst. 158(24), 2746–2756 (2007)
X. Lou, B. Cui, Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays. IEEE Trans. Syst. 37(3), 713–719 (2007)
W. Lu, T. Chen, Synchronization of coupled connected neural networks with delays. IEEE Trans. Circuits Syst. I 51(12), 2491–2503 (2004)
J. Lv, G. Chen, A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Autom. Control 50(6), 841–846 (2005)
L.M. Pecora, T.L. Carroll, G. Johnson, D. Mar, K.S. Fink, Synchronization stability in coupled oscillator arrays: solution for arbitrary configurations. Int. J. Bifurc. Chaos 10(2), 273–290 (2000)
S. Ruan, R. Filfil, Dynamics of a two-neuron system with discrete and distributed delays. Phys. D 191(3), 323–342 (2004)
Y. Sun, J. Cao, Z. Wang, Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70(13), 2477–2485 (2007)
W. Wang, J. Cao, Synchronization in an array of linearly coupled networks with time-varying delay. Phys. A 366, 197–211 (2006)
Z. Wang, J. Fang, X. Liu, Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fractals 36(2), 388–396 (2008)
Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fractals 32(1), 62–72 (2007)
Z. Wang, Y. Liu, F. Karl, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354(4), 288–297 (2006)
Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4), 299–308 (2005)
Z. Wang, H. Shu, J. Fang, X. Liu, Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal.: Real World Appl. 7(5), 1119–1128 (2006)
Z. Wang, H. Shu, Y. Liu, D.W.C. Ho, X. Liu, Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos Solitons Fractals 30(4), 886–896 (2006)
C.W. Wu, Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems. Phys. Lett. A 319(5–6), 495–503 (2003)
C.W. Wu, Synchronization in array of coupled nonlinear system with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuits Syst. 52(5), 282–286 (2005)
H. Xiang, J. Cao, Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays. Neurocomputing 72(7), 1702–1711 (2009)
H. Xiang, J. Wang, Exponential stability and periodic solution for fuzzy BAM neural networks with time varying delays. Appl. Math. J. Chin. Univ. 24(2), 157–166 (2009)
W. Yu, J. Cao, Synchronization control of stochastic delayed neural networks. Phys. A 373, 252–260 (2007)
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Zhou, W., Yang, J., Zhou, L., Tong, D. (2016). Exponential Stability and Synchronization Control of Neural Networks. In: Stability and Synchronization Control of Stochastic Neural Networks. Studies in Systems, Decision and Control, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47833-2_2
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DOI: https://doi.org/10.1007/978-3-662-47833-2_2
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