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Impulsive Synchronization of Stochastic Neural Networks via Controlling Partial States

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Abstract

In the paper, synchronization problem for stochastic neural networks are studied by impulsively controlling partial states. At each impulsive instant, only part of the states are controlled to realize the synchronization of impulsively coupled stochastic neural networks. By using the method of average impulsive interval, less conservative synchronization criteria are derived. The derived sufficient conditions are closely related to the parameters of system dynamics, impulsive gain, impulsive interval and the proportion of the controlled components. Finally, numerical example is given to illustrate the effectiveness of our theoretical results.

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References

  1. Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42(3):691–702

    Article  Google Scholar 

  2. Azar A, Vaidyanathan S (2015) Chaos modeling and control systems design. Springer, Berlin

    Book  MATH  Google Scholar 

  3. Cao J, Liang J, Lam J (2004) Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199(3–4):425–436

    Article  MathSciNet  MATH  Google Scholar 

  4. Cao J, Rakkiyappan R, Maheswari K, Chandrasekar A (2016) Exponential \(h_\infty \) filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Sci China Technol Sci 59(3):387–402

    Article  Google Scholar 

  5. Carli R, Zampieri S (2014) Network clock synchronization based on the second-order linear consensus algorithm. IEEE Trans Autom Control 59(2):409–422

    Article  MathSciNet  MATH  Google Scholar 

  6. Chandrasekar A, Rakkiyappan R, Cao J (2015) Impulsive synchronization of markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. Neural Netw 70:27–38

    Article  Google Scholar 

  7. Chen G, Dong X (1998) From chaos to order: methodologies, perspectives and applications. World Scientific, Singapore

    Book  MATH  Google Scholar 

  8. Guan Z, Liu Z, Feng G, Wang Y (2010) Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans Circuits Syst-I 57(8):2182–2195

    Article  MathSciNet  Google Scholar 

  9. Hooton E, Amann A (2012) Analytical limitation for time-delayed feedback control in autonomous systems. Phys Rev Lett 109(15):154101

    Article  Google Scholar 

  10. Hoppensteadt F, Izhikevich E (2000) Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans Neural Netw 11(3):734–738

    Article  Google Scholar 

  11. Hu C, Jiang H, Teng Z (2010) Globally exponential stability for delayed neural networks under impulsive control. Neural Process Lett 31(2):105–127

    Article  Google Scholar 

  12. Ji Y, Liu X, Ding F (2015) New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems. Nonlinear Dyn 79(1):1–9

    Article  MathSciNet  MATH  Google Scholar 

  13. Kapitaniak T, Kurths J (2014) Synchronized pendula: from huygens’ clocks to chimera states. Eur Phys J Spec Top 223(4):609–612

    Article  Google Scholar 

  14. Li X, Song S (2014) Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method. Commun Nonlinear Sci Numer Simul 19(10):3892–3900

    Article  MathSciNet  Google Scholar 

  15. Li Z, Wen C, Soh Y (2001) Analysis and design of impulsive control systems. IEEE Trans Autom Control 46(6):894–897

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu B (2008) Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Trans Autom Control 53(9):2128–2133

    Article  MathSciNet  Google Scholar 

  17. Liu Y, Chen H, Wu B (2014) Controllability of Boolean control networks with impulsive effects and forbidden states. Math Methods Appl Sci 37(1):1–9

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu Y, Lu J, Wu B (2015) Stability and \(L_2\)-gain performance for non-linear switched impulsive systems. IET Control Theory Appl 9(2):300–307

    Article  MathSciNet  Google Scholar 

  19. Liu Y, Zhao S, Lu J (2011) A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model. IEEE Trans Fuzzy Syst 19(2):393–398

    Article  Google Scholar 

  20. Lu J, Cao J, Ho D (2008) Adaptive stabilization and synchronization for chaotic Lur’e systems with-varying delay. IEEE Trans Circuits Syst-I 55(5):1347–1356

    Article  MathSciNet  Google Scholar 

  21. Lu J, Ding C, Lou J, Cao J (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Frankl Inst 352(11):5024–5041

    Article  MathSciNet  Google Scholar 

  22. Lu J, Ho D, Cao J (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46:1215–1221

    Article  MathSciNet  MATH  Google Scholar 

  23. Lu J, Kurths J, Cao J, Mahdavi N, Huang C (2012) Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans Neural Netw Learn Syst 23:285–292

    Article  Google Scholar 

  24. Lu J, Wang Z, Cao J, Ho D, Kurths J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22(07):1250176

    Article  MATH  Google Scholar 

  25. Nazhan S, Ghassemlooy Z, Busawon K (2016) Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback. Chaos 26(1):013109

    Article  MathSciNet  Google Scholar 

  26. Pan L, Guan Z, Zhou L (2013) Chaos multiscale-synchronization between two different fractional-order hyperchaotic systems based on feedback control. Int J Bifurc Chaos 23(08):1350146

    Article  MathSciNet  MATH  Google Scholar 

  27. Pecora L, Carroll T (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824

    Article  MathSciNet  MATH  Google Scholar 

  28. Pecora L, Carroll T (2015) Synchronization of chaotic systems. Chaos 25(9):097611

    Article  Google Scholar 

  29. Pereira T, Baptista M, Kurths J (2007) Detecting phase synchronization by localized maps: application to neural networks. Europhys Lett 77(4):40006

    Article  Google Scholar 

  30. Suykens J, Yang T, Chua L (1998) Impulsive synchronization of chaotic lur’e systems by measurement feedback. Int J Bifurc Chaos 8(06):1371–1381

    Article  MATH  Google Scholar 

  31. Vaidyanathan S, Rajagopal K (2012) Global chaos synchronization of hyperchaotic pang and hyperchaotic wang systems via adaptive control. Int J Soft Comput 7(1):28–37

    Article  Google Scholar 

  32. Wei H, Li R, Chen C, Tu Z. Stability analysis of fractional order complex-valued memristive neural networks with time delays. Neural Process Lett, 1–21

  33. Wen S, Zeng Z, Huang T, Zhang Y (2014) Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans Fuzzy Syst 22(6):1704–1713

    Article  Google Scholar 

  34. Wu B, Liu Y, Lu J (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Model 55(3):837–843

    Article  MathSciNet  MATH  Google Scholar 

  35. Wu C, Chua L (1994) A unified framework for synchronization and control of dynamical systems. Int J Bifurc Chaos 4:979–979

    Article  MathSciNet  MATH  Google Scholar 

  36. Xi Q (2016) Global exponential stability of cohen-grossberg neural networks with piecewise constant argument of generalized type and impulses. Neural Comput 28(1):229–255

    Article  Google Scholar 

  37. Yang R, Wu B, Liu Y (2015) A halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays. Appl Math Comput 265:696–707

    Article  MathSciNet  Google Scholar 

  38. Yang T (2001) Impulsive systems and control: theory and application. Nova Science, New York

    Google Scholar 

  39. Yang X, Cao J, Lu J (2011) Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal 12:2252–2266

    Article  MathSciNet  MATH  Google Scholar 

  40. Yang X, Cao J, Lu J (2013) Synchronization of randomly coupled neural networks with markovian jumping and time-delay. IEEE Trans Circuits Syst I 60(2):363–376

    Article  MathSciNet  Google Scholar 

  41. Zhang W, Tang Y, Miao Q, Du W (2013) Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans Neural Netw Learn Syst 24(8):1316–1326

    Article  Google Scholar 

  42. Zou F, Nossek J (1993) Bifurcation and chaos in cellular neural networks. IEEE Trans Circuits Syst-I 40(3):166–173

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Yuanyuan Li

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  1. Yuanyuan Li
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Correspondence to Yuanyuan Li.

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Li, Y. Impulsive Synchronization of Stochastic Neural Networks via Controlling Partial States. Neural Process Lett 46, 59–69 (2017). https://doi.org/10.1007/s11063-016-9568-0

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