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December  2016, 21(10): 3655-3667. doi: 10.3934/dcdsb.2016115

Finite-time synchronization of competitive neural networks with mixed delays

1. 

Department of Mathematics, Chongqing Normal University, Chongqing 401331, China, China

Received  September 2014 Revised  March 2016 Published  November 2016

In this paper, finite-time synchronization of competitive neural networks (CNNs) with bounded time-varying discrete and distributed delays (mixed delays) is investigated. A simple controller is added to response (slave) system such that it can be synchronized with the driving (master) CNN in a setting time. By introducing a suitable Lyapunov-Krasovskii's functional and utilizing some inequalities, several sufficient conditions are obtained to ensure the control object. Moreover, the setting time is explicitly given. Different from previous results, the setting is related to both the initial value of error system and the time delays. Finally, numerical examples are given to show the effectiveness of the theoretical results.
Citation: Tingting Su, Xinsong Yang. Finite-time synchronization of competitive neural networks with mixed delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3655-3667. doi: 10.3934/dcdsb.2016115
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show all references

References:
[1]

Applied Mathematical Modelling, 35 (2011), 3080-3091. doi: 10.1016/j.apm.2010.12.020.  Google Scholar

[2]

Journal of the Franklin Institute, 352 (2015), 4366-4381. doi: 10.1016/j.jfranklin.2015.06.006.  Google Scholar

[3]

Automatica, 50 (2014), 1944-1947. doi: 10.1016/j.automatica.2014.05.010.  Google Scholar

[4]

Commun. Nonlinear Sci. Numer. Simul, 17 (2012), 3708-3718. doi: 10.1016/j.cnsns.2012.01.021.  Google Scholar

[5]

Journal of the Franklin Institute, 347 (2010), 719-731. doi: 10.1016/j.jfranklin.2009.03.005.  Google Scholar

[6]

Nonlinear Dyn., 55 (2009), 55-65. doi: 10.1007/s11071-008-9344-4.  Google Scholar

[7]

Systems & Control Letters, 57 (2008), 561-566. doi: 10.1016/j.sysconle.2007.12.002.  Google Scholar

[8]

Nonlinear Analysis B: Real World Applications, 10 (2009), 928-942. doi: 10.1016/j.nonrwa.2007.11.014.  Google Scholar

[9]

Phys. Rev. Lett., 64 (1990), 821-824. doi: 10.1103/PhysRevLett.64.821.  Google Scholar

[10]

Neural Comput., 26 (2014), 2005-2024. doi: 10.1162/NECO_a_00629.  Google Scholar

[11]

Exp. Brain Res., (2009), 521-525. Google Scholar

[12]

Automatica, 34 (1998), 51-56. doi: 10.1016/S0005-1098(97)00174-X.  Google Scholar

[13]

Commun. Nonlinear Sci. Numer. Simul, 14 (2009), 3615-3628. doi: 10.1016/j.cnsns.2009.02.006.  Google Scholar

[14]

Nonlinearity, 21 (2008), 1579-1599. doi: 10.1088/0951-7715/21/7/011.  Google Scholar

[15]

Phys. Rev. E, (2001), 191-210.  Google Scholar

[16]

Applied Mathematical Modelling, 34 (2010), 3631-3641. doi: 10.1016/j.apm.2010.03.012.  Google Scholar

[17]

IEEE Trans. Circ. Syst. -I. Regular Paper, 59 (2012), 371-384. doi: 10.1109/TCSI.2011.2163969.  Google Scholar

[18]

SIAM J. Control Optim., 51 (2013), 3486-3510. doi: 10.1137/120897341.  Google Scholar

[19]

IEEE Transactions on Fuzzy Systems, 23 (2015), 2302-2316. doi: 10.1109/TFUZZ.2015.2417973.  Google Scholar

[20]

Chaos Solitons Fractals, 44 (2011), 817-826. doi: 10.1016/j.chaos.2011.06.006.  Google Scholar

[21]

Nonlinear Dyn., 73 (2013), 2313-2327. doi: 10.1007/s11071-013-0942-4.  Google Scholar

[22]

Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 1529-1543. doi: 10.1016/j.cnsns.2013.09.012.  Google Scholar

[23]

SIAM Journal on Applied Dynamical Systems, 9 (2010), 1303-1347. doi: 10.1137/100788872.  Google Scholar

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