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Dynamics Analysis of a Class of Memristor-Based Recurrent Networks with Time-Varying Delays in the Presence of Strong External Stimuli

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Abstract

In this paper, we investigate the dynamics problem about the memristor-based recurrent network with bounded activation functions and bounded time-varying delays in the presence of strong external stimuli. It is shown that global exponential stability of such networks can be achieved when the external stimuli are sufficiently strong, without the need for other conditions. A sufficient condition on the bounds of stimuli is derived for global exponential stability of memristor-based recurrent networks. And all the results are in the sense of Filippov solutions. Simulation results illustrate the uses of the criteria to ascertain the global exponential stability of specific networks.

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References

  1. Ahn C (2010) Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay. Inform Sci 180: 4582–4594

    Article  MATH  Google Scholar 

  2. Anthes G (2010) Memristor: pass or fail. Commun ACM 54: 22–24

    Article  Google Scholar 

  3. Bacciotti A, Rosier L (2005) Liapunov functions and stability in control theory. Springer, Berlin

    MATH  Google Scholar 

  4. Bao G, Zeng Z (2011) Analysis and design of associative memories based on recurrent neural network with discontinuous activation functions. Neurocomput. doi:10.1016/j.neucom.2011.08.026

  5. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I 52: 417–426

    Article  MathSciNet  Google Scholar 

  6. Cao J, Huang D, Qu Y (2005) Global robust stability of delayed recurrent neural networks. Chaos Solitions Fractals 23: 221–229

    Article  MATH  MathSciNet  Google Scholar 

  7. Cao J, Yuan K, Li H (2006) Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans Neural Netw 17: 1646–1651

    Article  Google Scholar 

  8. Chen A, Cao J, Huang L (2002) An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE Trans Circuits Syst I 49: 1028–1032

    Article  MathSciNet  Google Scholar 

  9. Chua L (1971) Memristor—the missing circuit element. IEEE Trans Circuit T-18: 507–519

    Article  Google Scholar 

  10. Filippov A (1988) Differential equations with discontinuous right-hand side, Mathematics its applications. Kluwer Academic, Boston

    Google Scholar 

  11. Forti M, Nistri P (2003) Global convergence of neural networks with discontinous neuron activations. IEEE Trans Circuit Syst I 50: 1421–1435

    Article  MathSciNet  Google Scholar 

  12. Gergel-Hackett N, Hamadani B, Suehle J, Richter C, Hacker C, Gundlach D (2009) A flexible solution-processed memristor. IEEE Electron Device Lett 30: 706–708

    Article  Google Scholar 

  13. Hu S, Wang J (2002) Global asmptotic stability and global exponential stability of continuous-time recurrent neural networks. IEEE Trans Automat Contr 47: 802–807

    Article  Google Scholar 

  14. Hu J, Wang J (2010) Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. In Proc IJCNN 2010, Spain

  15. Huang H, Cao J (2003) On global asymptotic stability of recurrent neural networks with time-varying delays. Appl Math Comput 142: 143–154

    Article  MATH  MathSciNet  Google Scholar 

  16. Huang H, Cao J, Wang J (2002) Global exponential stability and periodic solutions of recurrent neural networks with delays. Phys Lett A 298: 393–404

    Article  MATH  MathSciNet  Google Scholar 

  17. Huang H, Qu Y, Li H (2005) Robust stability analysis of switched Hopfield neural networks with time-varying dealy under uncertainty. Phys Lett A 345: 345–354

    Article  MATH  Google Scholar 

  18. Itoh M, Chua L (2008) Memristor oscillators. Int J Bifur Chaos 18: 3183–3206

    Article  MATH  MathSciNet  Google Scholar 

  19. Li T, Fei S, Zhu Q (2009) Design of exponential state estimator for neural networks with distributed delays. Nonlinear Anal Real World Appl 10: 1229–1242

    Article  MATH  MathSciNet  Google Scholar 

  20. Li X (2009) Global exponential stability for a class of neural networks. Appl Math Lett 22: 1235–1239

    Article  MATH  MathSciNet  Google Scholar 

  21. Li X, Chen Z (2009) Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Anal Real World Appl 10: 3253–3265

    Article  MATH  MathSciNet  Google Scholar 

  22. Lou X, Cui B (2007) Delay-dependent criteria for robust stability of uncertain switched hopfield neural networks. Int J Automat Comput 4: 304–314

    Article  Google Scholar 

  23. Niamsup P (2009) Stability of time-varying switched systems with time-varying delay. Nonlinear Anal Hybrid Syst 3: 631–639

    Article  MATH  MathSciNet  Google Scholar 

  24. Pershin Y, Ventra M (2010) Experimental demonstration of associative memory with memristive neural networks. Neural Netw 23: 881–886

    Article  Google Scholar 

  25. Rakkiyappan R, Balasubramaniam P, Cao J (2010) Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal Real World Appl 11: 122–130

    Article  MATH  MathSciNet  Google Scholar 

  26. Shen Y, Wang J (2008) An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 19: 528–531

    Article  Google Scholar 

  27. Strukov D, Snider G, Stewart D, Williams R (2008) The missing memristor found. Nature 453: 80–83

    Article  Google Scholar 

  28. Ventra M, Pershin Y, Chua L (2009) Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc IEEE 97: 1717–1724

    Article  Google Scholar 

  29. Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356: 346–352

    Article  MATH  Google Scholar 

  30. Wu H (2009) Stability analysis for periodic solution of neural networks with discontinuous neuron activations. Nonlinear Anal Real World Appl 10: 1717–1729

    Article  MATH  MathSciNet  Google Scholar 

  31. Wu L, Feng Z, Zheng W (2010) Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE Trans Neural Netw 21: 1396–1407

    Article  Google Scholar 

  32. Zeng Z, Wang J (2006) Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli. Neural Netw 19: 1528–1537

    Article  MATH  Google Scholar 

  33. Zeng Z, Wang J, Liao X (2003) Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I 50: 1353–1358

    Article  MathSciNet  Google Scholar 

  34. Zeng Z, Huang D, Wang Z (2005) Memory pattern analysis of cellular neural networks. Phys Lett A 342: 114–128

    Article  MATH  Google Scholar 

  35. Zeng Z, Wang J, Liao X (2005) Global asmptotic stability and global exponential stability of neural networks with unbounded time-varying delays. IEEE Trans Circuits Syst II 52: 168–173

    Article  Google Scholar 

  36. Zhang Y, Liu X, Shen X (2007) Stability of switched systems with time delay. Nonlinear Anal Hybrid Syst 1: 44–58

    Article  MATH  MathSciNet  Google Scholar 

  37. Zong G, Liu J, Zhang Y, Hou L (2010) Delay-range-dependent exponential stability criteria and decay estimation for switched Hopfield neural networks of neutral type. Nonlinear Anal Hybrid Syst 4: 583–592

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Shiping Wen & Zhigang Zeng

  2. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074, China

    Shiping Wen & Zhigang Zeng

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  1. Shiping Wen
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  2. Zhigang Zeng
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Correspondence to Zhigang Zeng.

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Wen, S., Zeng, Z. 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, 47–59 (2012). https://doi.org/10.1007/s11063-011-9203-z

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