• Previous Article
    Relative controllability of linear systems of fractional order with delay
  • MCRF Home
  • This Issue
  • Next Article
    Generalization on optimal multiple stopping with application to swing options with random exercise rights number
December  2015, 5(4): 827-844. doi: 10.3934/mcrf.2015.5.827

Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation

1. 

Department of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, 210096, Nanjing, China

2. 

Department of Applied Mathematics, Yanshan University, 066001, Qinhuangdao, China, China, China

Received  May 2014 Revised  January 2015 Published  October 2015

This paper is concerned with the projective synchronization issue for memristive neural networks with time-varying delays and stochastic perturbations. Based on LaSalle-type invariance principle of stochastic functional-differential equations, by applying Lyapunov functional approach, several sufficient conditions are developed to achieve the projective synchronization between the master-slave systems with time-varying delays under stochastic perturbation and adaptive controller. A numerical example and its simulation is given to show the effectiveness of the theoretical results in this paper.
Citation: Ruoxia Li, Huaiqin Wu, Xiaowei Zhang, Rong Yao. Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation. Mathematical Control & Related Fields, 2015, 5 (4) : 827-844. doi: 10.3934/mcrf.2015.5.827
References:
[1]

J. Aubin and H. Frankowska, Set-valued Analysis,, Birkhäuser, (1990).   Google Scholar

[2]

S. Bowong, F. M. Moukam Kakmeni and H. Fotsin, A new adaptive observer-based synchronization scheme for private communication,, Physics Letters A, 355 (2006), 193.  doi: 10.1016/j.physleta.2006.02.035.  Google Scholar

[3]

L. Chua, Memristor-the missing circut element,, IEEE Trans, 18 (1971), 507.   Google Scholar

[4]

T. Driscoll, J. Quinn, S. Klein, H. T. Kim, B. J. Kim, Y. V. Pershin, M. DiVentra and D. N. Basov, Memristive adaptive filters,, Appl. Phys. Lett., 97 (2010).  doi: 10.1063/1.3485060.  Google Scholar

[5]

A. Friedman, Stochastic Differential Equations and Applications,, Academic Press, (1976).   Google Scholar

[6]

L. Hu, H. J. Gao and W. X. Zheng, Novel stability of cellular neural networks with interval time-varying delay,, Neural Networks, 21 (2008), 1458.  doi: 10.1016/j.neunet.2008.09.002.  Google Scholar

[7]

X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations,, Journal of Mathematical Analysis and Applications, 268 (2002), 125.  doi: 10.1006/jmaa.2001.7803.  Google Scholar

[8]

L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems,, Physical Review Letters, 64 (1990), 821.  doi: 10.1103/PhysRevLett.64.821.  Google Scholar

[9]

Y. V. Pershin, S. La Fontaine and M. Di Ventra, Memristive model of amoeba learning, preprint,, 2009., ().   Google Scholar

[10]

Y. V. Pershin and M. Di Ventra, Experimental demonstration of associative memory with memristive neural networks,, Neural Networks, 23 (2010), 881.  doi: 10.1016/j.neunet.2010.05.001.  Google Scholar

[11]

Y. Shen and J. Wang, An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays,, Neural Networks, 19 (2008), 528.   Google Scholar

[12]

D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, The missing memristor found,, Nature, 453 (2008), 80.   Google Scholar

[13]

S. Sundar and A. Minai, Synchronization of randomly multiplexed chaotic systems with application to communication,, Physical Review Letters, 85 (2000), 5456.  doi: 10.1103/PhysRevLett.85.5456.  Google Scholar

[14]

J. M. Tour and T. He. Electronics, Electronics: The fourth element,, Nature, 453 (2008), 42.  doi: 10.1038/453042a.  Google Scholar

[15]

A. H. Wan, J. G. Peng and M. S. Wang, Exponential stability of a class of generalized neural networks with time-varying delays,, Neurocomputing, 69 (2006), 959.  doi: 10.1016/j.neucom.2005.06.012.  Google Scholar

[16]

R. L. Wang, Z. Tang and Q. P. Cao, A learning method in Hopfield neural network for combinatorial optimization problem,, Neurocomputing, 48 (2002), 1021.  doi: 10.1016/S0925-2312(02)00596-9.  Google Scholar

[17]

S. P. Wen, Z. G. Zeng and T. W. Huang, Adaptive synchronization of memristor-based Chua's circuits,, Physics Letters A, 376 (2012), 2775.   Google Scholar

[18]

S. P. Wen, Z. G. Zeng and T. W. Huang, Dynamic behaviors of memristor-based delayed recurrent networks,, Neural Computing and Applications, 23 (2013), 815.  doi: 10.1007/s00521-012-0998-y.  Google Scholar

[19]

A. L. Wu, S. P. Wen and Z. G. Zeng, Exponential synchronization of memristor-based recurrent neural networks with time delays,, Neurocomputing, 74 (2011), 3043.  doi: 10.1016/j.neucom.2011.04.016.  Google Scholar

[20]

A. L. Wu, S. P. Wen and Z. G. Zeng, Synchronization control of a class of memristor-based recurrent neural networks,, Information Sciences, 183 (2012), 106.  doi: 10.1016/j.ins.2011.07.044.  Google Scholar

[21]

A. L. Wu and Z. G. Zeng, Anti-synchronization control of a class of memristive recurrent neural networks,, Communications in Nonlinear Science and Numerical, 18 (2013), 373.  doi: 10.1016/j.cnsns.2012.07.005.  Google Scholar

[22]

S. Y. Xu, Y. M. Chu and J. W. Lu, New results on global exponential stability of recurrent neural networks with time-varying delays,, Physics. Letters. A, 352 (2006), 371.  doi: 10.1016/j.physleta.2005.12.031.  Google Scholar

[23]

G. D. Zhang and Y. Shen, Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays,, Information Sciences, 232 (2013), 386.  doi: 10.1016/j.ins.2012.11.023.  Google Scholar

[24]

H. G. Zhang and G. Wang, New criteria of global exponential stability for a class of generalized neural networks with time-varying delays,, Neurocomputing, 70 (2007), 2486.  doi: 10.1016/j.neucom.2006.08.002.  Google Scholar

[25]

L. Zhang, Y. Zhang and J. L. Yu, Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions,, Neural Networks, 19 (2008), 158.  doi: 10.1109/TNN.2007.904015.  Google Scholar

[26]

L. Zhang and Y. Zhang, Selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function,, Neural Networks, 22 (2011), 1021.  doi: 10.1109/TNN.2011.2132762.  Google Scholar

[27]

L. Zhang, Y. Zhang, S. L. Zhang and P. A. Heng, Activity invariant sets and exponentially stable attractors of linear threshold discrete-time recurrent neural networks,, Automatic Control, 54 (2009), 1341.  doi: 10.1109/TAC.2009.2015552.  Google Scholar

[28]

D. M. Zhou and J. D. Cao, Globally exponential stability conditions for cellular neural networks with time-varying delays,, Applied Mathematics and Computation, 131 (2002), 487.  doi: 10.1016/S0096-3003(01)00162-X.  Google Scholar

show all references

References:
[1]

J. Aubin and H. Frankowska, Set-valued Analysis,, Birkhäuser, (1990).   Google Scholar

[2]

S. Bowong, F. M. Moukam Kakmeni and H. Fotsin, A new adaptive observer-based synchronization scheme for private communication,, Physics Letters A, 355 (2006), 193.  doi: 10.1016/j.physleta.2006.02.035.  Google Scholar

[3]

L. Chua, Memristor-the missing circut element,, IEEE Trans, 18 (1971), 507.   Google Scholar

[4]

T. Driscoll, J. Quinn, S. Klein, H. T. Kim, B. J. Kim, Y. V. Pershin, M. DiVentra and D. N. Basov, Memristive adaptive filters,, Appl. Phys. Lett., 97 (2010).  doi: 10.1063/1.3485060.  Google Scholar

[5]

A. Friedman, Stochastic Differential Equations and Applications,, Academic Press, (1976).   Google Scholar

[6]

L. Hu, H. J. Gao and W. X. Zheng, Novel stability of cellular neural networks with interval time-varying delay,, Neural Networks, 21 (2008), 1458.  doi: 10.1016/j.neunet.2008.09.002.  Google Scholar

[7]

X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations,, Journal of Mathematical Analysis and Applications, 268 (2002), 125.  doi: 10.1006/jmaa.2001.7803.  Google Scholar

[8]

L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems,, Physical Review Letters, 64 (1990), 821.  doi: 10.1103/PhysRevLett.64.821.  Google Scholar

[9]

Y. V. Pershin, S. La Fontaine and M. Di Ventra, Memristive model of amoeba learning, preprint,, 2009., ().   Google Scholar

[10]

Y. V. Pershin and M. Di Ventra, Experimental demonstration of associative memory with memristive neural networks,, Neural Networks, 23 (2010), 881.  doi: 10.1016/j.neunet.2010.05.001.  Google Scholar

[11]

Y. Shen and J. Wang, An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays,, Neural Networks, 19 (2008), 528.   Google Scholar

[12]

D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, The missing memristor found,, Nature, 453 (2008), 80.   Google Scholar

[13]

S. Sundar and A. Minai, Synchronization of randomly multiplexed chaotic systems with application to communication,, Physical Review Letters, 85 (2000), 5456.  doi: 10.1103/PhysRevLett.85.5456.  Google Scholar

[14]

J. M. Tour and T. He. Electronics, Electronics: The fourth element,, Nature, 453 (2008), 42.  doi: 10.1038/453042a.  Google Scholar

[15]

A. H. Wan, J. G. Peng and M. S. Wang, Exponential stability of a class of generalized neural networks with time-varying delays,, Neurocomputing, 69 (2006), 959.  doi: 10.1016/j.neucom.2005.06.012.  Google Scholar

[16]

R. L. Wang, Z. Tang and Q. P. Cao, A learning method in Hopfield neural network for combinatorial optimization problem,, Neurocomputing, 48 (2002), 1021.  doi: 10.1016/S0925-2312(02)00596-9.  Google Scholar

[17]

S. P. Wen, Z. G. Zeng and T. W. Huang, Adaptive synchronization of memristor-based Chua's circuits,, Physics Letters A, 376 (2012), 2775.   Google Scholar

[18]

S. P. Wen, Z. G. Zeng and T. W. Huang, Dynamic behaviors of memristor-based delayed recurrent networks,, Neural Computing and Applications, 23 (2013), 815.  doi: 10.1007/s00521-012-0998-y.  Google Scholar

[19]

A. L. Wu, S. P. Wen and Z. G. Zeng, Exponential synchronization of memristor-based recurrent neural networks with time delays,, Neurocomputing, 74 (2011), 3043.  doi: 10.1016/j.neucom.2011.04.016.  Google Scholar

[20]

A. L. Wu, S. P. Wen and Z. G. Zeng, Synchronization control of a class of memristor-based recurrent neural networks,, Information Sciences, 183 (2012), 106.  doi: 10.1016/j.ins.2011.07.044.  Google Scholar

[21]

A. L. Wu and Z. G. Zeng, Anti-synchronization control of a class of memristive recurrent neural networks,, Communications in Nonlinear Science and Numerical, 18 (2013), 373.  doi: 10.1016/j.cnsns.2012.07.005.  Google Scholar

[22]

S. Y. Xu, Y. M. Chu and J. W. Lu, New results on global exponential stability of recurrent neural networks with time-varying delays,, Physics. Letters. A, 352 (2006), 371.  doi: 10.1016/j.physleta.2005.12.031.  Google Scholar

[23]

G. D. Zhang and Y. Shen, Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays,, Information Sciences, 232 (2013), 386.  doi: 10.1016/j.ins.2012.11.023.  Google Scholar

[24]

H. G. Zhang and G. Wang, New criteria of global exponential stability for a class of generalized neural networks with time-varying delays,, Neurocomputing, 70 (2007), 2486.  doi: 10.1016/j.neucom.2006.08.002.  Google Scholar

[25]

L. Zhang, Y. Zhang and J. L. Yu, Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions,, Neural Networks, 19 (2008), 158.  doi: 10.1109/TNN.2007.904015.  Google Scholar

[26]

L. Zhang and Y. Zhang, Selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function,, Neural Networks, 22 (2011), 1021.  doi: 10.1109/TNN.2011.2132762.  Google Scholar

[27]

L. Zhang, Y. Zhang, S. L. Zhang and P. A. Heng, Activity invariant sets and exponentially stable attractors of linear threshold discrete-time recurrent neural networks,, Automatic Control, 54 (2009), 1341.  doi: 10.1109/TAC.2009.2015552.  Google Scholar

[28]

D. M. Zhou and J. D. Cao, Globally exponential stability conditions for cellular neural networks with time-varying delays,, Applied Mathematics and Computation, 131 (2002), 487.  doi: 10.1016/S0096-3003(01)00162-X.  Google Scholar

[1]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017

[2]

Qiang Fu, Yanlong Zhang, Yushu Zhu, Ting Li. Network centralities, demographic disparities, and voluntary participation. Mathematical Foundations of Computing, 2020, 3 (4) : 249-262. doi: 10.3934/mfc.2020011

[3]

Stefan Ruschel, Serhiy Yanchuk. The Spectrum of delay differential equations with multiple hierarchical large delays. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 151-175. doi: 10.3934/dcdss.2020321

[4]

Shipra Singh, Aviv Gibali, Xiaolong Qin. Cooperation in traffic network problems via evolutionary split variational inequalities. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020170

[5]

Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020379

[6]

Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323

[7]

Wenbin Li, Jianliang Qian. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020073

[8]

Zhenzhen Wang, Tianshou Zhou. Asymptotic behaviors and stochastic traveling waves in stochastic Fisher-KPP equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020323

[9]

Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299

[10]

Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264

[11]

Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020046

[12]

Serena Dipierro, Benedetta Pellacci, Enrico Valdinoci, Gianmaria Verzini. Time-fractional equations with reaction terms: Fundamental solutions and asymptotics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 257-275. doi: 10.3934/dcds.2020137

[13]

Guido Cavallaro, Roberto Garra, Carlo Marchioro. Long time localization of modified surface quasi-geostrophic equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020336

[14]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

[15]

Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020444

[16]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[17]

Xuhui Peng, Rangrang Zhang. Approximations of stochastic 3D tamed Navier-Stokes equations. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5337-5365. doi: 10.3934/cpaa.2020241

[18]

Yahia Zare Mehrjerdi. A new methodology for solving bi-criterion fractional stochastic programming. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020054

[19]

Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020047

[20]

Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020432

2019 Impact Factor: 0.857

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]