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Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays

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Abstract

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen–Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.

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References

  • Strukov DB, Snider GS, Stewart GR, Williams RS (2008) The missing memristor found. Nature 453:80–83

    Article  CAS  PubMed  Google Scholar 

  • Chua LO (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18:507–519

    Article  Google Scholar 

  • Itoh M, Chua LO (2010) Autoassociative memory cellular neural networks. Int J Bifurc Chaos 20:3225–3266

    Article  Google Scholar 

  • Oskoee EN, Sahimi M (2011) Electric currents in networks of interconnected memristors. Phys Rev E 83:031105

    Article  Google Scholar 

  • Corinto F, Ascoli A, Gilli M (2011) Nonlinear dynamics of memristor oscillators. IEEE Trans Circuit Syst 58:1323–1336

    Article  Google Scholar 

  • Buscarino A, Fortuna L, Frasca M, Gambuzza LV (2012) A chaotic circuit based on Hewlett-Packard memristor. Chaos 22:023136

    Article  PubMed  Google Scholar 

  • Pershin YV, Ventra MD (2012) Experimental demonstration of associative memory with memristive neural networks. Neural Netw 23:881–886

    Article  Google Scholar 

  • Pershin Y, Slipko V, Ventra MD (2013) Complex dynamics and scale invariance of one-dimensional memristive networks. Phys Rev E 87:022116

    Article  Google Scholar 

  • Yang X, Cao J, Yu W (2014) Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays. Cogn Neurodynamics 8:239–249

    Article  Google Scholar 

  • Qi J, Li C, Huang T (2014) Stability of delayed memristive neural networks with time-varying impulses. Cogn Neurodynamics 8:429–436

    Article  Google Scholar 

  • Stilwell DJ, Bollt EM, Roberson DG (2006) Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM J Appl Dynam Syst 5:140–156

    Article  Google Scholar 

  • Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824

    Article  PubMed  Google Scholar 

  • Ojalvo JG, Roy R (2001) Spatiotemporal communication with synchronized optical chaos. Phys Rev Lett 86:5204–5207

    Article  Google Scholar 

  • Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Phys Rev Lett 76:1804

    Article  CAS  PubMed  Google Scholar 

  • Kim CM, Rim S, Kye WH, Ryu JW, Park YJ (2003) Anti-synchronization of chaotic oscillators. Phys Lett A 320:39–46

    Article  CAS  Google Scholar 

  • Rulkov NF, Sushchik MM, Tsimring LS (1995) Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E 51:980

    Article  Google Scholar 

  • Runzi L (2008) Adaptive function project synchronization of Rössler hyperchaotic system with uncertain parameters. Phys Lett A 372:3667–3671

    Article  CAS  Google Scholar 

  • Abdurahman A, Jiang H, Teng Z (2014) Function projective synchronization of impulsive neural networks with mixed time-varying delays. Nonlinear Dyn 78:2627–2638

    Article  Google Scholar 

  • Cao J, Liang J (2004) Boundedness and stability for Cohen–Grossberg neural network with time-varying delay. J Math Anal Appl 296:665–685

    Article  Google Scholar 

  • Zhang Z, Cao J, Zhou D (2014) Novel LMI-based condition on global asymptotic stability for a class of Cohen–Grossberg bam networks with extended activation functions. IEEE Trans Neural Netw Learn Syst 25:1161–1172

    Article  Google Scholar 

  • Lisena B (2011) Dynamical behavior of impulsive and periodic Cohen–Grossberg neural networks. Nonlinear Anal 74:4511–4519

    Article  Google Scholar 

  • Zhu Q, Cao J (2010) Adaptive synchronization of chaotic Cohen–Grossberg neural networks with mixed time delays. Nonlinear Dyn 61:517–534

    Article  Google Scholar 

  • Abdurahman A, Jiang H (2015) The existence and stability of the anti-periodic solution for delayed Cohen–Grossberg neural networks with impulsive effects. Neurocomputing 149:22–28

    Article  Google Scholar 

  • Rakkiyappan R, Velmurugan G, Cao J (2015) Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cogn Neurodynamics 9:145–177

    Article  CAS  Google Scholar 

  • Zhang G, Shen Y, Wang L (2013) Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. Neural Netw 46:1–8

    Article  PubMed  Google Scholar 

  • Wu A, Wen S, Zeng Z (2012) Synchronization control of a class of memristor-based recurrent neural networks. Inf Sci 183:106–116

    Article  Google Scholar 

  • Wen S, Bao G, Zeng Z, Chen Y, Huang T (2013) Global exponential synchronization of memristor-based recurrent neural networks with time-varying delay. Neural Netw 48:195–203

    Article  PubMed  Google Scholar 

  • Li N, Cao J (2015) New synchronization criteria for memristor-based networks: adaptive control and feedback control schemes. Neural Netw 61:1–9

    Article  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Zhang G, Shen Y (2014) Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw 55:1–10

    Article  CAS  PubMed  Google Scholar 

  • Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 69:20–28

    Article  PubMed  Google Scholar 

  • Bao H, Cao J (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9

    Article  PubMed  Google Scholar 

  • Bai J, Yu Y, Wang S, Song Y (2012) Modified projective synchronization of uncertain fractional order hyperchaotic systems. Commun Nonlinear Sci Numer Simul 17:1921–1928

    Article  Google Scholar 

  • Chandrasekar A, Rakkiyappan R, Cao J, Lakshmanan 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

    Article  CAS  PubMed  Google Scholar 

  • Wan Y, Cao J (2015) Periodicity and synchronization of coupled memristive neural networks with supremums. Neurocomputing 159:137–143

    Article  Google Scholar 

  • Clarke FH, Ledyaev YS, Stem RJ, Wolenski RR (1998) Nonsmooth analysis and control theory. Springer, New York

    Google Scholar 

  • Filippov AF (1988) Differential equations with discontinuous righthand sides. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundations of P.R. China (Grant Nos. 61473244, 61164004 and 11461069), the Excellent Doctor Innovation Program of Xinjiang University (Grant No. XJUBSCX-2013006) and the Graduate Research Innovation Program of Xinjiang (Grant No. XJGRI2014013).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Ürümqi, 830046, Xinjiang, People’s Republic of China

    Abdujelil Abdurahman, Haijun Jiang & Kaysar Rahman

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  1. Abdujelil Abdurahman
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  2. Haijun Jiang
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  3. Kaysar Rahman
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Correspondence to Abdujelil Abdurahman.

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Abdurahman, A., Jiang, H. & Rahman, K. Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. Cogn Neurodyn 9, 603–613 (2015). https://doi.org/10.1007/s11571-015-9352-2

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