Skip to main content
Log in

Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, the existence and the exponential stability of piecewise differentiable pseudo-almost periodic solutions for a class of impulsive neutral high-order Hopfield neural networks with mixed time-varying delays and leakage delays are established by employing the fixed point theorem, Lyapunov functional method and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Aouiti C, M’hamdi MS, Touati A (2016) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett. doi:10.1007/s11063-016-9515-0

  2. Li Y, Wang C, Li X (2014) Existence and global exponential stability of almost periodic solution for high-order BAM neural networks with delays on time scales. Neural Process Lett 39(3):247–268

    Article  Google Scholar 

  3. Yu Y, Cai M (2008) Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks. Math Comput Model 47(9–10):943–951

    Article  MathSciNet  MATH  Google Scholar 

  4. Xiao B, Meng H (2009) Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural. Appl Math Model 33(1):532–542

    Article  MathSciNet  MATH  Google Scholar 

  5. Xiang H, Yan K-M, Wang B-Y (2006) Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Phys Lett A 352(4–5):341–349

    Article  MATH  Google Scholar 

  6. Xu B, Liu X, Teo K L (2009) Global exponential stability of impulsive high-order Hopfield type neural networks with delays. Comput Math Appl 57(11–12):1959–1967

    Article  MathSciNet  MATH  Google Scholar 

  7. Cheng L, Zhang A, Qiu J, Chen X, Yang C, Chen X (2015) Existence and stability of periodic solution of high-order discrete-time Cohen–Grossberg neural networks with varying delays. Neurocomput Part C 149:1445–1450

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Ren F, Cao J (2007) Periodic oscillation of higher-order bidirectional associative memory neural networks with periodic coefficients and delays. Nonlinearity 20(3):605–629

    Article  MathSciNet  MATH  Google Scholar 

  10. Jinde C, 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 March 59(3):387–402

    Article  Google Scholar 

  11. Cao J, Ho Daniel WC, Huang X (2007) LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay. Nonlinear Anal 66(7):1558–1572

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang Y, Cao J (2013) Exponential stability of stochastic higher-order BAM neural networks with reaction diffusion terms and mixed time-varying delays. Neurocomputing 119:192–200

    Article  Google Scholar 

  13. Ren F, Cao J (2007) Periodic solutions for a class of higher-order Cohen–Grossberg type neural networks with delays. Comput Math Appl 54(6):826–839

    Article  MathSciNet  MATH  Google Scholar 

  14. Xiang H, Cao J (2009) Almost periodic solution of Cohen–Grossberg neural networks with bounded and unbounded delays. Nonlinear Anal Real World Appl 10(4):2407–2419

    Article  MathSciNet  MATH  Google Scholar 

  15. Cao J, Song Q (2006) Stability in Cohen Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19(7):1601–1617

    Article  MathSciNet  MATH  Google Scholar 

  16. Tu Z, Cao J, Hayat T (2016) Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays. Neurocomputing 171(1):524–531

    Article  Google Scholar 

  17. Pan L, Cao J (2011) Anti-periodic solution for delayed cellular neural networks with impulsive effects. Nonlinear Anal Real World Appl 12(6):3014–3027

    MathSciNet  MATH  Google Scholar 

  18. Rakkiyappan R, Balasubramaniam P, Cao J (2010) Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal Real World Appl 11(1):122–130

    Article  MathSciNet  MATH  Google Scholar 

  19. Xiao B (2009) Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl Math Lett 22(4):528–533

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang W (2012) Existence and stability of almost periodic solutions for a class of generalized Hopfield neural networks with time-varying neutral delays. J Appl Math Inf 30(5–6):1051–1065

    MathSciNet  MATH  Google Scholar 

  21. Bai C (2008) Global stability of almost periodic solution of Hopfield neural networks with neutral time-varying delays. Appl Math Comput 203(1):72–79

    MathSciNet  MATH  Google Scholar 

  22. Bai C (2009) Existence and stability of almost periodic solutions of hopfield neural networks with continuously distributed delays. Nonlinear Anal 71(11):5850–5859

    Article  MathSciNet  MATH  Google Scholar 

  23. Huang H, Cao J, Wang J (2002) Global exponential stability and periodic solutions of recurrent neural networks with delays. Phys Lett A 298(5–6):393–404

    Article  MathSciNet  MATH  Google Scholar 

  24. Jiang H, Cao J (2006) Global exponential stability of periodic neural networks with time-varying delays. Neurocomputing 70(1):343–350

    Article  Google Scholar 

  25. Xiang H, Cao J (2009) Almost periodic solutions of recurrent neural networks with continuously distributed delays. Nonlinear Anal 71(12):6097–6108

    Article  MathSciNet  MATH  Google Scholar 

  26. Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325(2):1117–1132

    Article  MathSciNet  MATH  Google Scholar 

  27. Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7):1709–1726

    Article  MathSciNet  MATH  Google Scholar 

  28. Li C, Huang T (2009) On the stability of nonlinear systems with leakage delay. J Frankl Inst 346(4):366–377

    Article  MathSciNet  MATH  Google Scholar 

  29. Gao J, Wang Q-R, Zhang L-W (2014) Existence and stability of almost periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl Math Comput 237:639–649

    MathSciNet  MATH  Google Scholar 

  30. Chuanyi Z (1994) Pseudo almost periodic solutions of some differential equations. J Math Anal Appl 181(1):6276

    MathSciNet  Google Scholar 

  31. Chuanyi Z (1995) Pseudo almost periodic solutions of some differential equations, II. J Math Anal Appl 192(2):543–561

    Article  MathSciNet  MATH  Google Scholar 

  32. Shao J, Wang L, Ou C (2009) Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activaty functions. Appl Math Model 33(6):2575–2581

    Article  MathSciNet  MATH  Google Scholar 

  33. Li Y, Wang C (2011) Almost periodic functions on time scales and applications. Discrete Dyn Nat Soc. Article ID 727068, 20 pages

  34. Xia Z (2015) Pseudo almost periodic mild solution of nonautonomous impulsive integro-differential equations. Mediterr J Math 12(1):1–22

    Article  MathSciNet  Google Scholar 

  35. Liu J, Zhang C (2013) Composition of piecewise pseudo almost periodic functions and applications to abstract impulsive differential equations. Adv Differ Equ 2013:11. doi:10.1186/1687-1847-2013-11

  36. Chérif F (2014) Pseudo almost periodic solutions of impulsive differential equations with delay. Differ Equ Dyn Syst 22(1):73–91

    Article  MathSciNet  MATH  Google Scholar 

  37. Jiang H, Teng Z (2004) Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Netw 17(10):1415–1425

    Article  MATH  Google Scholar 

  38. Zhao W (2008) Dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays. Nonlinear Anal Real World Appl 9(3):1024–1037

    Article  MathSciNet  MATH  Google Scholar 

  39. Lin Z, Lin Y-X (2000) Linear systems, exponential dichotomy, and structure of sets of hyperbolic points. World Scientific, Singapore

    Book  MATH  Google Scholar 

  40. Zhang C (2003) Almost periodic type functions and ergodicity. Science Press, Beijing

    Book  MATH  Google Scholar 

  41. Wang P, Li Y, Ye Y (2016) Almost periodic solutions for neutral-type neural networks with the delays in the leakage term on time scales. Math Methods Appl Sci (2 Feb 2016). doi:10.1002/mma.3857

  42. Stamov TG, Stamova IM (2007) Almost periodic solutions for impulsive neural networks with delay. Appl Math Model 31(7):1263–1270

    Article  MATH  Google Scholar 

  43. Stamov TG (2008) Existence of almost periodic solutions for impulsive cellular neural networks. Rocky Mt J Math 38(4):1271–1284

    Article  MathSciNet  MATH  Google Scholar 

  44. Ylmaz E (2014) Almost periodic solutions of impulsive neural networks at non-prescribed moments of time. Neurocomputing 141:148–152

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chaouki Aouiti.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C. Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput & Applic 29, 477–495 (2018). https://doi.org/10.1007/s00521-016-2558-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2558-3

Keywords

Navigation