Skip to main content
SpringerLink
Log in

Almost periodic solutions of quaternion-valued neutral type high-order Hopfield neural networks with state-dependent delays and leakage delays

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we consider the existence and global exponential stability of almost periodic solutions for a class of quaternion-valued neutral type neural networks with state-dependent delays and leakage delays by a direct approach. That is, without decomposing the considered quaternion-valued systems into real-valued systems, by using the contraction mapping fixed point theorem, we obtain the existence of almost periodic solutions of the considered networks with state-dependent delays and leakage delays, and by the counter-evidence method, we obtain the global exponential stability of almost periodic solutions of the considered networks with discrete delays and leakage delays. When the time delays in the considered systems are proportional time delays, our existence results are still true. At the same time, when the considered systems degenerate into real-valued or complex-valued systems, our results are still new.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Liu X, Teo K L, Xu B (2005) Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 16(6):1329–1339

    Article  Google Scholar 

  2. Liu X, Wang Q (2008) Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 19(1):71–79

    Article  MathSciNet  Google Scholar 

  3. Qiu J (2010) Dynamics of high-order Hopfield neural networks with time delays. Neurocomputing 73 (4-6):820–826

    Article  Google Scholar 

  4. Li Y, Yang L (2014) Almost automorphic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales. Appl Math Comput 242:679–693

    MathSciNet  MATH  Google Scholar 

  5. Li Y, Meng X, Xiong L (2017) Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales. Int J Machine Learn Cyber 8 (6):1915–1927

    Article  Google Scholar 

  6. Xu C, Li P (2017) Pseudo almost periodic solutions for high-order Hopfield neural networks with time-varying leakage delays. Neural Process Lett 46(1):41–58

    Article  MathSciNet  Google Scholar 

  7. Xu C, Li P (2017) Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays. Chaos Solitons Fractals 96:139–144

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhao L, Li Y, Li B (2018) Weighted pseudo-almost automorphic solutions of high-order Hopfield neural networks with neutral distributed delays. Neural Comput Appl 29(7):513–527

    Article  Google Scholar 

  9. Li Y, Wang H, Meng X (2019) Almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks with time-varying and distributed delays. IMA J Math Control Inform 36(3):983–1013

    Article  MathSciNet  Google Scholar 

  10. Li Y, Qin J, Li B (2019) Anti-periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays. Neural Process Lett 49(3):1217–1237

    Article  Google Scholar 

  11. Aouiti C, Dridi F (2019) Piecewise asymptotically almost automorphic solutions for impulsive non-autonomous high-order Hopfield neural networks with mixed delays. Neural Comput Appl 31(9):5527–5545

    Article  Google Scholar 

  12. Aouiti C (2018) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl 29(9):477–495

    Article  Google Scholar 

  13. Alimi AM, Aouiti C, Chérif F, Dridi F, M’hamdi MS (2018) Dynamics and oscillations of generalized high-order Hopfield Neural Networks with mixed delays. Neurocomputing 321:274–295

    Article  Google Scholar 

  14. Aouiti C, Assali EA (2019) Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays. Neural Comput Appl 31(11):7781–7803

    Article  Google Scholar 

  15. Alimi AM, Aouiti C, Miaadi F (2019) Effect of leakage delay on finite time boundedness of impulsive high-order neutral delay generalized neural networks. Neurocomputing 347:34–45

    Article  Google Scholar 

  16. Zhang A (2018) Pseudo almost periodic high-order cellular neural networks with complex deviating arguments. Int J Machine Learn Cyber 10(2):301–309

    Article  Google Scholar 

  17. Ozcan N (2018) New conditions for global stability of neutral-type delayed Cohen-Grossberg neural networks. Neural Netw 106:1–7

    Article  MATH  Google Scholar 

  18. Tu Z, Cao J, Alsaedi A, Alsaadi F (2017) Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw 88:125–133

    Article  MATH  Google Scholar 

  19. Ali MS, Saravanan S, Rani ME, Elakkia S, Cao J, Alsaedi A, Hayat T (2017) Asymptotic stability of Cohen-Grossberg BAM neutral type neural networks with distributed time varying delays. Neural Process Lett 46(3):991–1007

    Article  Google Scholar 

  20. Shi K, Zhong S, Zhu H, Liu X, Zeng Y (2015) New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays. Neurocomputing 168:896–907

    Article  Google Scholar 

  21. Arik S (2019) A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays. J Frankl Instit 356(1):276–291

    Article  MathSciNet  MATH  Google Scholar 

  22. Arbi A, Cao J (2017) Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Neural Process Lett 46(2):719–745

    Article  Google Scholar 

  23. Xu D, Tan M (2017) Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays. Nonlinear Dyn 89(2):819–832

    Article  MATH  Google Scholar 

  24. Ozcan N (2019) Stability analysis of Cohen-Grossberg neural networks of neutral-type: Multiple delays case. Neural Netw 113:20–27

    Article  MATH  Google Scholar 

  25. Aouiti C, Gharbia IB, Cao J, Alsaedi A (2019) Dynamics of impulsive neutral-type BAM neural networks. J Frankl Instit 356(4):2294–2324

    Article  MathSciNet  MATH  Google Scholar 

  26. Ali MS, Saravanan S, Zhu Q (2017) Finite-time stability of neutral-type neural networks with random time-varying delays. Int Syst Sci 48(15):3279–3295

    Article  MathSciNet  MATH  Google Scholar 

  27. Li Y, Meng X (2017) Existence and global exponential stability of pseudo almost periodic solutions for neutral type quaternion-valued neural networks with delays in the leakage term on time scales. Complexity, Article ID 9878369, 15 pages

  28. Kong F, Fang X (2018) Pseudo almost periodic solutions of discrete-time neutral-type neural networks with delays. Appl Intell 48(10):3332–3345

    Article  Google Scholar 

  29. Kong F, Fang X, Liang Z (2018) Dynamic behavior of a class of neutral-type neural networks with discontinuous activations and time-varying delays. Appl Intell 48(12):4834–4854

    Article  Google Scholar 

  30. Manivannan R, Cao Y (2018) Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays. J Frankl Instit 355(9):3990–4014

    Article  MathSciNet  MATH  Google Scholar 

  31. Huang C, Cao J (2018) Impact of leakage delay on bifurcation in high-order fractional BAM neural networks. Neural Netw 98:223–235

    Article  MATH  Google Scholar 

  32. Zhu H, Rakkiyappan R, Li X (2018) Delayed state-feedback control for stabilization of neural networks with leakage delay. Neural Netw 105:249–255

    Article  MATH  Google Scholar 

  33. Samidurai R, Sriraman R, Zhu S (2019) Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays. Neurocomputing 338:262–273

    Article  Google Scholar 

  34. Qin J, Li Y (2018) New results on exponential stability of competitive neural networks with multi-proportional delays. Asian J Control, in press. https://doi.org/10.1002/asjc.1926

  35. Li N, Cao J (2018) Global dissipativity analysis of quaternion-valued memristor-based neural networks with proportional delay. Neurocomputing 321:103–113

    Article  Google Scholar 

  36. Son DT, Trinh H (2018) On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE Trans Neural Netw Learn Syst 29(1):225–231

    Article  MathSciNet  Google Scholar 

  37. Wang W (2018) Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays. Fuzzy Sets Systems 338:40–49

    Article  MathSciNet  MATH  Google Scholar 

  38. Li Y, Liu P (2004) Existence and stability of positive periodic solution for BAM neural networks with delays. Math Comput Modelling 40(7-8):757–770

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang A (2017) Pseudo almost periodic solutions for SICNNs with oscillating leakage coefficients and complex deviating arguments. Neural Process Lett 45(1):183–196

    Article  Google Scholar 

  40. Zhou Q (2016) Pseudo almost periodic solutions for SICNNs with leakage delays and complex deviating arguments. Neural Process Lett 44(2):375–386

    Article  MathSciNet  Google Scholar 

  41. Michel AN, Farrell JA (1990) Associative memories via artificial neural networks. IEEE Contr Syst Mag 10(3):6–17

    Article  Google Scholar 

  42. Cichocki A, Amari SI (2002) Adaptive blind signal and image processing: learning algorithms and applications. Wiley, New York

    Book  Google Scholar 

  43. Mishra D, Kalra PK (2007) Modified hopfield neural network approach for solving nonlinear algebraic equations. Eng Lett 14(1):135–142

    Google Scholar 

  44. Ripley BD (2007) Pattern recognition and neural networks. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  45. Tagliarini GA, Christ JF, Page EW (1991) Optimization using neural networks. IEEE Transactions Comput 40:1347–1358

    Article  Google Scholar 

  46. Ma T, Kuang P, Tian W (2019) An improved recurrent neural networks for 3d object reconstruction. Appl Intell, in press. https://doi.org/10.1007/s10489-019-01523-3

  47. Kim J, Kim HJ, Kim H (2019) Fraud detection for job placement using hierarchical clusters-based deep neural networks. Appl Intell 49(8):2842–2861

    Article  Google Scholar 

  48. Suliman A, Omaro BS (2018) Applying Bayesian regularization for acceleration of Levenberg-Marquardt based neural network training. Int J Int Multimed Artif Intell 5(1):68–72

    Google Scholar 

  49. Goli A, Zare HK, Moghaddam RT, Sadeghieh A (2019) An improved artificial intelligence based on gray wolf optimization and cultural algorithm to predict demand for dairy products: a case study. Int J Int Multimed Artif Intell 5(6):15–22

    Google Scholar 

  50. Jha S, Dey A, Kumar R, Kumar V (2019) A novel approach on visual question answering by parameter prediction using faster region based convolutional neural network. Int J Int Multimed Artif Intell 5(5):30–37

    Google Scholar 

  51. Bouchra N, Aouatif A, Mohammed N, Nabil H (2019) Deep belief network and auto-encoder for face classification. Int J Int Multimed Artif Intell 5(5):22–29

    Google Scholar 

  52. Li Y, Qin J (2018) Existence and global exponential stability of periodic solutions for quaternion-valued cellular neural networks with time-varying delays. Neurocomputing 292:91–103

    Article  Google Scholar 

  53. Li Y, Fang Y, Qin J (2019) Anti-periodic synchronization of quaternion-valued generalized cellular neural networks with time-varying delays and impulsive effects. Int J Control Autom Syst 17(5):1191–1208

    Article  Google Scholar 

  54. Li Y, Qin J, Li B (2019) Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects. Math Meth Appl Sci 42(1):5–23

    Article  MathSciNet  MATH  Google Scholar 

  55. Huo N, Li Y (2018) Antiperiodic solutions for quaternion-valued shunting inhibitory cellular neural networks with distributed delays and impulses. Complexity, Article ID 6420256, 12 pages

  56. Li Y, Meng X (2018) Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term. Int J Syst Sci 49(11):2490–2505

    Article  MathSciNet  Google Scholar 

  57. Li Y, Li B, Yao S, Xiong L (2018) The global exponential pseudo almost periodic synchronization of quaternion-valued cellular neural networks with time-varying delays. Neurocomputing 303:75–87

    Article  Google Scholar 

  58. Meng X, Li Y (2018) Pseudo almost periodic solutions for quaternion-valued cellular neural networks with discrete and distributed delays. J Ineq Appl 2018:245

    Article  MathSciNet  Google Scholar 

  59. You X, Song Q, Liang J, Liu Y, Alsaadi FE (2018) Global μ-stability of quaternion-valued neural networks with mixed time-varying delays. Neurocomputing 290:12–25

    Article  Google Scholar 

  60. Chen X, Song Q, Li Z, Zhao Z, Liu Y. (2017) Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons. IEEE Trans Neural Netw Learn Syst 29(7):2769–2781

    MathSciNet  Google Scholar 

  61. Li Y, Wang H (2018) Almost periodic synchronization of quaternion-valued shunting inhibitory cellular neural networks with mixed delays via state-feedback control. PloS One 13(6):e0198297

    Article  Google Scholar 

  62. Li Y, Wang H, Meng X (2019) Almost periodic synchronization of fuzzy cellular neural networks with time-varying delays via state-feedback and impulsive control. Int J Appl Math Comput Sci 29(2):337–349

    Article  MathSciNet  MATH  Google Scholar 

  63. Fink AM (1974) Almost periodic differential equations. Springer, Berlin

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, Yunnan, 650091, People’s Republic of China

    Yongkun Li & Jianglian Xiang

  2. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan, 650500, People’s Republic of China

    Bing Li

Authors
  1. Yongkun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianglian Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongkun Li.

Ethics declarations

Conflict of interests

The authors declare that they have no conflicts of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is supported by the National Natural Science Foundation of China under Grant No. 11861072 and the Applied Basic Research Programs of Science and Technology Department of Yunnan Province under Grant No. 2019FB003.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Xiang, J. & Li, B. Almost periodic solutions of quaternion-valued neutral type high-order Hopfield neural networks with state-dependent delays and leakage delays. Appl Intell 50, 2067–2078 (2020). https://doi.org/10.1007/s10489-020-01634-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-020-01634-2

Keywords

Search

Navigation