Abstract
In this paper, the stability problem of stochastic memristor-based recurrent neural networks with mixed time-varying delays is investigated. Sufficient conditions are established in terms of linear matrix inequalities which can guarantee that the stochastic memristor-based recurrent neural networks are asymptotically stable and exponentially stable in the mean square, respectively. Two examples are given to demonstrate the effectiveness of the obtained results.
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References
Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory CT–18(5):507–519
Strukov DB, Snider GS, Stewart GR, Williams RS (2008) The missing memristor found. Nature 453(7191):80–83
Tour JM, He T (2008) The fourth element. Nature 453(7191):42–43
Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64(2):209–223
Chua L (2011) Resistance switching memories are memristors. Appl Phys A 102(4):765–783
Hu J, Wang J (2010) Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. In: 2010 International joint conference on neural networks, Barcelona, Spain, pp 1–8
Wen S, Zeng Z, Huang T (2012) Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 97:233–240
Zhang G, Shen Y, Sun J (2012) Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 97:149–154
Guo Z, Wang J, Yan Z (2013) Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:158–172
Wen S, Zeng Z (2012) Dynamics analysis of a class of memristor-based recurrent networks with time-varying delays in the presence of strong external stimuli. Neural Process Lett 35(1):47–59
Li J, Hu M, Guo L (2014) Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays. Neurocomputing 138:92–98
Mathiyalagan K, Anbuvithya R, Sakthivel R, Park JH, Prakash P (2015) Reliable stabilization for memristor-based recurrent neural networks with time-varying delays. Neurocomputing 153:140–147
Chandraselcar A, Ralclciyappan R, Cao J, Lalcshmanan S (2014) Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Neural Netw 57:79–93
Wang W, Li L, Peng H, Xiao J, Yang Y (2014) Synchronization control of memristor-based recurrent neural networks with perturbations. Neural Netw 53:8–14
Wu A, Wen S, Zeng Z (2012) Synchronization control of a class of memristor-based recurrent neural networks. Inf Sci 183(1):106–116
Wu A, Zeng Z (2013) Anti-synchronization control of a class of memristive recurrent neural networks. Commun Nonlinear Sci Numer Simul 18(2):373–385
Anbuvithya R, Mathiyalagan K, Sakthivel R, Prakash P (2015) Non-fragile synchronization of memristive BAM networks with random feedback gain fluctuations. Commun Nonlinear Sci Numer Simul 29(1–3):427–440
Jiang M, Mei J, Hu J (2015) New results on exponential synchronization of memristor-based chaotic neural networks. Neurocomputing 156:60–67
Jiang M, Wang S, Mei J, Shen Y (2015) Finite-time synchronization control of a class of memristor-based recurrent neural networks. Neural Netw 63:133–140
Zhang G, Shen Y, Yin Q, Sun J (2013) Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays. Inf Sci 232:386–396
Wang L, Shen Y (2014) New results on passivity analysis of memristor-based neural networks with time-varying delays. Neurocomputing 144:208–214
Wu A, Zeng Z (2014) Passivity analysis of memristive neural networks with different memductance functions. Commun Nonlinear Sci Numer Simul 19(1):274–285
Ralclciyappan R, Sivaranjani K, Velmurugan G (2014) Passivity and passification of memristor-based complex-valued recurrent neural networks with interval time-varying delays. Neurocomputing 144:391–407
Wu A, Zeng Z (2014) Exponential passivity of memristive neural networks with time delays. Neural Netw 49:11–18
Meng Z, Xiang Z (2015) Passivity analysis of memristor-based recurrent neural networks with mixed time-varying delays. Neurocomputing 165:270–279
Blythe S, Mao X, Liao X (2001) Stability of stochastic delay neural networks. J Frankl Inst 338(4):481–495
Wang Z, Shu H, Fang J, Liu X (2006) Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal Real World App 7(5):1119–1128
Wan L (2009) Exponential stability of stochastic Hopfield neural networks with delays and Markovian switching. In: Fifth international conference on natural computation, 14–16 Aug. Tianjin, China, Vol 3, pp 1–652
Hu J, Zhong S, Liang L (2006) Exponential stability analysis of stochastic delayed cellular neural network. Chaos Solitons Fract 27(4):1006–1010
Huang H, Ho D, Lam J (2005) Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays. IEEE Trans Circuits Syst II Express Briefs 52(5):251–255
Wan L, Sun J (2005) Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys Lett A 343(4):306–318
Wan L (2009) Exponential stability of stochastic fuzzy recurrent neural networks with time-varying delays and diffusion terms. In: 2009 Fifth international conference on natural computation, 14–16 Aug. Tianjin, China, Vol 4, pp 232–236
Sakthivel R, Raja R, Anthoni SM (2011) Exponential stability for delayed stochastic bidirectional associative memory neural networks with markovian jumping and impulses. J Optim Theory Appl 150(1):166–187
Mathiyalagan K, Sakthivel R, Anthoni SM (2012) Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks. Phys Lett A 376(8–9):901–912
Rakkiyappan R, Balasubramaniam P, Lakshmanan S (2008) Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. Phys Lett A 372(32):5290–5298
Rakkiyappan R, Balasubramaniam P (2008) Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl Math Comput 198(2):526–533
Sakthivel S, Samidurai R, Anthoni SM (2010) Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects. J Optim Theory Appl 147(3):583–596
Ma L, Da F (2009) Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays. Phys Lett A 373(25):2154–2161
Wang Z, Fang J, Liu X (2008) Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fract 36(2):388–396
Rakkiyappan R, Balasubramaniam P (2009) LMI conditions for stability of stochastic recurrent neural networks with distributed delays. Chaos Solitons Fract 40(4):1688–1696
Wu Z, Shi P, Su H, Chu J (2011) Delay-dependent stability analysis for switched neural networks with time-varying delay. IEEE Trans Syst Man Cybern B 41(6):1522–1530
Boyd SP, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. Society for Industrial and Applied, Philadelphia
Gu KQ (2000) An integral inequality in the stability problem of time-delay systems. In: Proceeding of the 39th IEEE conference on decision and control, December, Sydney, Australia, pp 2805–2810
Kwon OM, Lee SM, Park JH, Cha EJ (2012) New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput 218(19):9953–9964
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This work is supported by the National Natural Science Foundation of China under Grant No. 61273120.
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Meng, Z., Xiang, Z. Stability analysis of stochastic memristor-based recurrent neural networks with mixed time-varying delays. Neural Comput & Applic 28, 1787–1799 (2017). https://doi.org/10.1007/s00521-015-2146-y
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DOI: https://doi.org/10.1007/s00521-015-2146-y