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Periodic Solution and Strange Attractor in Impulsive Hopfield Networks with Time-Varying Delays

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IAENG Transactions on Engineering Technologies

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 229))

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Abstract

By constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for impulsive Hopfield neural networks with time-varying delays. Our condition extends and generalizes a known condition for the global exponential periodicity of continuous Hopfield neural networks with time-varying delays. Further the numerical simulation shows that our system can occur many forms of complexities including gui strange attractor and periodic solution.

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References

  1. Abou-El-Ela AMA, Sadekand AI, Mahmoud AM (2012) Existence and uniqueness of a periodic solution for third-order delay differential equation with two deviating arguments. IAENG Int J Appl Math, 42:1 \({\rm {IJAM}}\_42\_1\_02\)

    Google Scholar 

  2. Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuoustime additive Hopfield-type neural networks with impulses. J Math Anal Appl 290(2):436–451

    Article  MathSciNet  MATH  Google Scholar 

  3. Arika S, Tavsanoglu V (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68:161–176

    Article  Google Scholar 

  4. Bainov DD, Simenov PS (1989) Systems with impulse effect: stability theory and applications. Ellis Horwood, Chichester

    MATH  Google Scholar 

  5. Cao J, Jiang Q (2004) An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys Lett A 330(3–4):203–213

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng Y, Yan Y, Gui Z (2012) Existence and stability of periodic solution in impulsive Hopfield networks with time-varying delays. Lecture notes in engineering and computer science: Proceedings of the world congress on engineering WCE 2012, 4–6 July 2012 U.K , London, pp 18–23

    Google Scholar 

  7. Gopalsamy K, Zhang BG (1989) On delay differential equation with impulses. J Math Anal Appl 139(1):110–C122

    Article  MathSciNet  MATH  Google Scholar 

  8. Gui Z, Ge W (2006) Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses. Chaos 16(3):1–10

    Article  MathSciNet  Google Scholar 

  9. Gui Z, Yang XS (2006) Stability and existence of periodic solutions of periodic cellular neural networks. Comput Math Appl 52(12):1657–1670

    Article  MathSciNet  MATH  Google Scholar 

  10. Gui Z, Ge W (2007) Impulsive effect of continuous-time neural networks under pure structural variations. Int J Bifurcat Chaos 17(6):2127–2139

    Article  MathSciNet  MATH  Google Scholar 

  11. Gui Z, Yang XS, Ge W (2007) Periodic solution for nonautonomous bidirectional associative memory neural networks with impulses. Neurocomputing 70(13–15):2517–2527

    Article  Google Scholar 

  12. Lakshmikantham V, Baino DD, Simeonov P-S (1989) Theory of impulsive differential equations. World Scientific, Singapore

    Book  MATH  Google Scholar 

  13. Li S, Liao X, Li C (2005) Hopf bifurcation of a two-neuron network with different discrete time delays. Int J Bifurcat Chaos 15(5):1589–1601

    Article  MathSciNet  MATH  Google Scholar 

  14. Li Y (2005) Global exponential stability of BAM neural networks with delays and impulses. Chaos, Solitons Fractals 24(1):279–285

    MathSciNet  MATH  Google Scholar 

  15. Li Y, Xing W, Lu L (2006) Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solitons Fractals 27(2):437–445

    Article  MathSciNet  MATH  Google Scholar 

  16. Song Y, Peng Y, Wei J (2008) Bifurcations for a predator-prey system with two delays. J Math Anal Appl 337(1):466–479

    Article  MathSciNet  MATH  Google Scholar 

  17. Xu S, Lam J, Zou Y (2005) Delay-dependent approach to stabilization of time-delay chaotic systems via standard and delayed feedback controllers. Int J Bifurcat Chaos 15(4):1455–1465

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang X, Liao X, Evans DJ, Tang Y (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays. Phys Lett A 343(1–3):108–116

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. The School of Science, Beijing Forestry University, Beijing, 100083, People’s Republic of China

    Yanxia Cheng

  2. The School of Mathematics and Statistics, Hainan Normal University, Haikou, Hainan, 571158, People’s Republic of China

    Yan Yan

  3. Department of Software Engineering, Hainan College of Software Technology, QiongHai, Hainan, 571400, People’s Republic of China

    Zhanji Gui

Authors
  1. Yanxia Cheng
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  2. Yan Yan
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  3. Zhanji Gui
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Corresponding author

Correspondence to Yanxia Cheng .

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Editors and Affiliations

  1. , Department of Multimedia Engineering, Mokpo National University, Dorim-ri, MuanGun 61, Chonnam, 534-729, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. IAENG Secretariat, Hung To Road, Unit 1, 1/F 37-39, Hong Kong, Hong Kong SAR

    Sio-long Ao

  3. School of Engineering, Applied Mathematics and Computing, Cranfield University, College Road, Cranfield, MK43 0AL, Bedfordshire, United Kingdom

    Len Gelman

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Cheng, Y., Yan, Y., Gui, Z. (2013). Periodic Solution and Strange Attractor in Impulsive Hopfield Networks with Time-Varying Delays. In: Yang, GC., Ao, Sl., Gelman, L. (eds) IAENG Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 229. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6190-2_2

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  • DOI: https://doi.org/10.1007/978-94-007-6190-2_2

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6189-6

  • Online ISBN: 978-94-007-6190-2

  • eBook Packages: EngineeringEngineering (R0)

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