Abstract
This paper studies the problem of global exponential stabilization and synchronization for impulsive Hopfield-type neural networks with impulse time window. By using the stability theory of impulsive dynamical systems, some sufficient conditions guaranteeing the global exponential stabilization and synchronization of Hopfield-type NNs are derived. The main innovation embodies that the impulsive instants are no longer limited at fixed instants, but suggested to be at some certain time intervals, named by impulse time windows. We shall show that impulses occurring randomly in impulse time windows can still stabilize and/or synchronize the considered neural networks under certain suitable assumptions. Two numerical examples are also given to illustrate the effectiveness of theoretical results.
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References
Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554–2558
Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci 81(10):3088–3092
Young SS, Scott PD, Nasrabadi NM (1997) Object recognition using multilayer Hopfield neural network. IEEE Trans Image Process 6(3):357–372
Huang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10(6):1366–1374
Joya G, Atencia MA, Sandoval F (2002) Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing 43(1–4):219–237
Wang Z, Liu Y, Fraser K, Liu X (2006) Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys Lett A 354(4):288–297
Peng JG, Xu ZB, Qiao H (2005) A critical analysis on global convergence of Hopfield-type neural networks. IEEE Trans Circuits Syst I Regul Pap 52(4):804–814
Blythe S, Mao XR, Liao XX (2001) Stability of stochastic delay neural networks. J Frankl Inst 338(4):481–495
Lu WL, Chen TP (2004) Synchronization of coupled connected neural networks with delays. IEEE Trans Circuits Syst I Regul Pap 51(12):2491–2503
Chen GR, Zhou J, Liu ZR (2004) Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. Int J Bifurc Chaos 14(7):2229–2240
Yang T, Chua LO (1997) Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans Circuits Syst I Fundam Theory Appl 44(10):976–988
Yang ZC, Xu DY (2005) Stability analysis of delay neural networks with impulsive effects. EEE Trans Circuits Syst II Express Briefs 52(8):517–521
Khadra A, Liu XZ, Shen X (2005) Impulsively synchronizing chaotic systems with delay and applications to secure communication. Automatica 41(9):1491–1502
Zheng S, Dong GG, Bi QS (2009) Impulsive synchronization of complex networks with non-delayed and delayed coupling. Phys Lett A 373(46):4255–4259
Guan ZH, Liu ZW, Feng G, Wang YW (2010) Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans Circuits Syst I Regul Pap 57(8):2182–2195
Xu DY, Yang ZC (2005) Impulsive delay differential inequality and stability of neural networks. J Math Anal Appl 305(1):107–120
Yang ZC, Xu DY (2006) Existence and exponential stability of periodic solution for impulsive delay differential equations and applications. Nonlinear Anal Theory Methods Appl 64(1):130–145
Stamov GT, Stamova IM (2007) Almost periodic solutions for impulsive neural networks with delay. Appl Math Model 31(7):1263–1270
Yang J, Zhong SM, Luo WP (2008) Mean square stability analysis of impulsive stochastic differential equations with delays. J Comput Appl Math 216(2):474–483
Fu XL, Li XD (2009) Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. J Comput Appl Math 231(1):187–199
Yang YX, Liao XF, Evans DJ, Tang YY (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays. Phys Lett A 343(1–3):28–35
Li CD, Shen YY, Feng G (2008) Stabilizing effects of impulses in delayed BAM neural networks. IEEE Trans Circuits Syst II Express Briefs 55(12):1284–1288
Song QK, Zhang JY (2008) Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays. Nonlinear Anal Real World Appl 9(2):500–510
Liu XZ, Qing W (2008) Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 19(1):71–79
Song QK, Wang ZD (2008) Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Phys A 387(13):3314–3326
Zhang HG, Dong M, Wang YC, Sun N (2010) Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping. Neurocomputing 43(13–15):2689–2695
Li CD, Feng GG, Liao XF (2011) Stabilizing effects of impulses in discrete-time delayed neural networks. IEEE Trans Neural Netw 22(2):323–329
Raja R, Sakthivel R, Anthoni S, Kim H (2011) Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays. Int J Appl Math Comput Sci 21(1):127–135
Bao HB, Cao JD (2011) Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters. Commun Nonlinear Sci Numer Simul 16(9):3786–3791
Li CJ, Li CD, Liao XF et al (2011) Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 74(10):1541–1550
Li XD, Rakkiyappah R (2013) Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 18(6):1515–1523
Li CJ, Yu W, Huang T (2014) Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach. Neural Netw 54:85–94
Li XD, Song SJ (2014) Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method. Commun Nonlinear Sci Numer Simul 19(10):3892–3900
Wang X, Li CD, Huang TW, Chen L (2014) Impulsive exponential synchronization of randomly coupled neural networks with markovian jumping and mixed model-dependent time delays. Neural Netw 60:25–32
Chen WH, Lu XM, Zheng WX (2015) Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks. IEEE Trans Neural Netw Learn Syst 26(4):734–748
Feng YM, Yu JZ, Li CD, Huang TW, Che HJ (2015) Linear impulsive control system with impulse time windows. J Vib Control. doi:10.1177/1077546315575465
Cai SM, Zhou J, Xiang L, Liu ZR (2008) Robust impulsive synchronization of complex delayed dynamical networks. Phys Lett A 372(30):4990–4995
Zheng S, Dong GG, Bi QS (2009) Impulsive synchronization of complex networks with non-delayed and delayed coupling. Phys Lett A 373(46):4255–4259
Guan ZH, Liu ZW, Feng G, Wang YW (2010) Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans Circuits Syst I Regul Pap 57(8):2182–2195
Zhou J, Wu QJ, Xiang L, Cai SM, Liu ZR (2011) Impulsive synchronization seeking in general complex delayed dynamical networks. Nonlinear Anal Hybrid Syst 5(3):513–524
Yang XS, Cao JD, Lu JQ (2011) Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal Real World Appl 12(4):2252–2266
Yang XS, Cao JD, Lu JQ (2012) Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and Impulsive control. IEEE Trans Circuits Syst I Regular Pap 59(2):371–384
Das PK II, Schieve WC, Zeng ZJ (1991) Chaos in an effective four-neuron neural network. Phys Lett A 161(1):60–66
Cheng CJ, Liao TL, Yan JJ, Hwang CC (2005) Synchronization of neural networks by decentralized feedback control. Phys Lett A 338(1):29–35
Acknowledgments
This research is supported by the Natural Science Foundation of China (Grant No. 63174078), the Fundamental Research Funds for the Central Universities (XDJK2012C069), and NPRP grant # NPRP 4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation).
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Zhou, Y., Li, C., Huang, T. et al. Impulsive stabilization and synchronization of Hopfield-type neural networks with impulse time window. Neural Comput & Applic 28, 775–782 (2017). https://doi.org/10.1007/s00521-015-2105-7
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DOI: https://doi.org/10.1007/s00521-015-2105-7