Abstract
This paper pays attention to the synchronization control methodology for stochastic memristive system. On the framework of Lyapunov functional, stability theory and free-weighting matrices technique, some brand-new solvability criteria are established to ensure the exponential synchronization goal of the target model. Considering the introduce of some free-weighting matrices, the obtained synchronization verdict will be much more applicable. Finally, the living example is included to show the effectiveness of the presented methodology.






Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Chua LO (1971) Memristor-the missing circut element. IEEE Trans Circuit Theory 18:507–519
Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64:209–223
Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83
Yang X, Feng Z, Feng J, Cao J (2017) Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw 85:157–164
Cohen MA, Grossberg S (1987) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Systems Man Cybern 13:815–826
Chen S, Cao J (2012) Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch. Nonlinear Dyn 67:1397–1406
Haykin S (1998) Neural networks: a comprehensive foundation. Prentice-Hall, Englewood Cliffs
Yang X, Cao J (2014) Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations. Appl Math Comput 227:480–493
Zhang X, Lv X, Li X (2017) Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control. Nonlinear Dyn 90:2199–2207
Song Q, Cao J (2008) Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. J Franklin Inst 345:39–59
Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61:2256–2261
Lu J, Ho DWC (2011) Stabilization of complex dynamical networks with noise disturbance under performance constraint. Nonlinear Anal Ser B Real World Appl 12:1974–1984
Wang Z, Ding S, Huang Z, Zhang H (2015) Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method. IEEE Trans Neural Netw Learn Syst 129:2029–2035
Lu J, Ding C, Lou J, Cao J (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Franklin Inst 352:5024–5041
Li X, Zhu Q, O’Regan D (2014) pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs. J Franklin Inst 351:4435–4456
Lu J, Ho DWC (2010) Globally exponential synchronization and synchronizability for general dynamical networks. IEEE Trans Syst Man Cybern 40:350–361
Li Y, Li B, Liu Y, Lu J, Wang Z, Alsaadi F (2018) Set stability and set stabilization of switched Boolean networks with state-based switching. IEEE Access 6:35624–35630
Zhang G, Shen Y (2013) New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 24:1701–1707
Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Franklin Inst 355:6520–6530
Li Y, Zhong J, Lu J, Wang Z (2018) On robust synchronization of drive-response boolean control networks with disturbances. Math Probl Eng. https://doi.org/10.1155/2018/1737685
Lu J, Wang Z, Cao J, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22:1250176
Yan M, Qiu J, Chen X, Chen X, Yang C, Zhang A, Alsaadi F (2018) The global exponential stability of the delayed complex-valued neural networks with almost periodic coefficients and discontinuous activations. Neural Process Lett 48:577–601
Yang X, Cao J, Liang J (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 28:1878–1888
Li R, Cao J, Alsaedi A, Ahmad B (2017) Passivity analysis of delayed reaction-diffusion Cohen–Grossberg neural networks via Hardy-Poincarè inequality. J Franklin Inst 354:3021–3038
Wang J, Wu H, Huang T (2015) Passivity-based synchronization of a class of complex dynamical networks with time-varying delay. Automatica 56:105–112
Ding S, Wang Z, Zhang H (2018) Dissipativity analysis for stochastic memristive neural networks with time-varying delays: a discrete-time case. IEEE Trans Neural Netw Learn Syst 29:618–630
Li R, Wei H (2016) Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms via sampled data control. Int J Mach Learn Cybern 7:157–169
Zhang L, Yang Y (2018) Different impulsive effects on synchronization of fractional-order memristive BAM neural networks. Nonlinear Dyn. https://doi.org/10.1007/s11071-018-4188-z
Zhang L, Yang Y, Wang F (2017) Lag synchronization for fractional-order memristive neural networks via period intermittent control. Nonlinear Dyn 89:367–381
Li R, Wu H, Zhang X, Yao R (2015) Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation. Math Control Relat Fields 5:827–844
Wang W, Li L, Peng H, Kurths J, Xiao J, Yang Y (2016) Finite-time anti-synchronization control of memristive neural networks with stochastic perturbations. Neural Process Lett 43:49–63
Li R, Cao J (2016) Finite-time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Trans Neural Netw Learn Syst 28:2924–2935
Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia
Yu M, Wang W, Luo X, Liu L, Yuan M (2017) Exponential antisynchronization control of stochastic memristive neural networks with mixed time-varying delays based on novel delay-dependent or delay-independent adaptive controller. Math Probl Eng. https://doi.org/10.1155/2017/8314757
Liu H, Wang Z, Shen B, Liu X (2017) Event-triggered \(H_\infty \) state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case. IEEE Trans Neural Netw Learn Syst 29:3726–3737
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was supported by National Natural Science Foundation of China (Grant Nos. 61803247, 61802243, 61273311 and 61173094), Project Funded by China Postdoctoral Science Foundation 2018M640948, the Fundamental Research Funds for the Central Universities under Grant No. GK201903003, the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002.
Rights and permissions
About this article
Cite this article
Li, R., Gao, X. & Cao, J. Exponential Synchronization of Stochastic Memristive Neural Networks with Time-Varying Delays. Neural Process Lett 50, 459–475 (2019). https://doi.org/10.1007/s11063-019-09989-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-019-09989-5