[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Piecewise Pseudo Almost-Periodic Solutions of Impulsive Fuzzy Cellular Neural Networks with Mixed Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This article examines the existence of the unique piecewise pseudo almost periodic for impulsive fuzzy cellular neural networks by using the contraction mapping principle and piecewise pseudo almost periodic function theory. Further, sufficient certain conditions for their global exponential stability are produced through the use of differential inequality and generalized Gronwall–Bellman inequality. Our results are new and complement some previously known ones. Two examples and their numerical simulations are performed to ensure our theoretical results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn 10(6):573–591

    MathSciNet  Google Scholar 

  2. Duan L, Fang X, Huang C (2018) Global exponential convergence in a delayed almost periodic Nicholson’s blowflies model with discontinuous harvesting. Math Methods Appl Sci 41(5):1954–1965

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  4. Yang W (2014) Periodic solution for fuzzy Cohen–Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients. Neural Process Lett 40(1):51–73

    Google Scholar 

  5. Cai Z, Huang J, Huang L (2018) Periodic orbit analysis for the delayed Filippov system. Proc Am Math Soc 146(11):4667–4682

    MathSciNet  MATH  Google Scholar 

  6. Chua LO, Yang L (1988) Cellular neural networks: applications. IEEE Trans Circuits Syst 35(10):1273–1290

    MathSciNet  Google Scholar 

  7. Baldi P, Sadowski P (2018) Learning in the machine: recirculation is random backpropagation. Neural Netw 108:479–494

    Google Scholar 

  8. Costarelli D, Vinti G (2016) Pointwise and uniform approximation by multivariate neural network operators of the max-product type. Neural Netw 81:81–90

    MATH  Google Scholar 

  9. Costarelli D, Vinti G (2017) Convergence for a family of neural network operators in orlicz spaces. Math Nachr 290(2–3):226–235

    MathSciNet  MATH  Google Scholar 

  10. Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117

    Google Scholar 

  11. Ahmad S, Stamova IM (2008) Global exponential stability for impulsive cellular neural networks with time-varying delays. Nonlinear Anal Theory Methods Appl 69(3):786–795

    MathSciNet  MATH  Google Scholar 

  12. De Vries B, Principe JC (1992) The gamma model—a new neural model for temporal processing. Neural Netw 5(4):565–576

    Google Scholar 

  13. Huang C, Zhang H, Huang L (2019) Almost periodicity analysis for a delayed Nicholson’s blowflies model with nonlinear density-dependent mortality term. Commun Pure Appl Anal 18(6):3337–3349

    MathSciNet  Google Scholar 

  14. Huang C, Zhang H (2019) Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method. Int J Biomath 12(02):1950016

    MathSciNet  MATH  Google Scholar 

  15. Aouiti C, abed Assali E, Cao J, Alsaedi A (2018) Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays. Int J Syst Sci 49(10):2202–2214

    MathSciNet  Google Scholar 

  16. Huang C, Cao J, Wen F, Yang X (2016) Stability analysis of SIR model with distributed delay on complex networks. PLoS ONE 11(8):e0158813

    Google Scholar 

  17. Aouiti C, Coirault P, Miaadi F, Moulay E (2017) Finite time boundedness of neutral high-order hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing 260:378–392

    Google Scholar 

  18. Aouiti C, Dridi F (2018) \((\mu,\nu )\)-Pseudo-almost automorphic solutions for high-order Hopfield bidirectional associative memory neural networks. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3651-6

    Article  Google Scholar 

  19. Meng F, Li K, Song Q, Liu Y, Alsaadi FE (2019) Periodicity of Cohen–Grossberg-type fuzzy neural networks with impulses and time-varying delays. Neurocomputing 325:254–259

    Google Scholar 

  20. Aouiti C, Ben Gharbia I, Cao J, M’hamdi MS, Alsaedi A (2018) Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms. Chaos Solitons Fractals 107:111–127

    MathSciNet  MATH  Google Scholar 

  21. Yang T, Yang LB (1996) The global stability of fuzzy cellular neural network. IEEE Trans Circuits Syst I Fundam Theory Appl 43(10):880–883

    MathSciNet  Google Scholar 

  22. Tang Y (2019) Exponential stability of pseudo almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Process Lett 49(2):851–861

    Google Scholar 

  23. Tang R, Yang X, Wan X, Zou Y, Cheng Z, Fardoun HM (2019) Finite-time synchronization of nonidentical BAM discontinuous fuzzy neural networks with delays and impulsive effects via non-chattering quantized control. Commun Nonlinear Sci Numer Simul 78:104893

    MathSciNet  Google Scholar 

  24. Duan L, Huang L, Guo Z, Fang X (2017) Periodic attractor for reaction–diffusion high-order Hopfield neural networks with time-varying delays. Comput Math Appl 73(2):233–245

    MathSciNet  MATH  Google Scholar 

  25. Bao H (2018) Existence and stability of anti-periodic solutions for FCNNs with time-varying delays and impulsive effects on time scales. Int J Comput Sci Math 9(5):474–483

    MathSciNet  Google Scholar 

  26. ZZhang Q, Yang L, Liu J (2014) Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen–Grossberge neural networks on time scales. Math Slovaca 64(1):119–138

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  28. Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal Real World Appl 14(1):559–566

    MathSciNet  MATH  Google Scholar 

  29. Xia Z (2016) Pseudo almost periodic mild solution of nonautonomous impulsive integro-differential equations. Mediterr J Math 13(3):1065–1086

    MathSciNet  MATH  Google Scholar 

  30. Li Y, Chen X, Zhao L (2009) Stability and existence of periodic solutions to delayed Cohen–Grossberg BAM neural networks with impulses on time scales. Neurocomputing 72(7–9):1621–1630

    Google Scholar 

  31. Li Yt, Yang Cb (2006) Global exponential stability analysis on impulsive BAM neural networks with distributed delays. J Math Anal Appl 324(2):1125–1139

    MathSciNet  MATH  Google Scholar 

  32. Samidurai R, Sakthivel R, Anthoni SM (2009) Global asymptotic stability of BAM neural networks with mixed delays and impulses. Appl Math Comput 212(1):113–119

    MathSciNet  MATH  Google Scholar 

  33. Xia Y, Huang Z, Han M (2008) Existence and globally exponential stability of equilibrium for BAM neural networks with impulses. Chaos Solitons Fractals 37(2):588–597

    MathSciNet  MATH  Google Scholar 

  34. Wang W, Liu B (2014) Global exponential stability of pseudo almost periodic solutions for SICNNs with time-varying leakage delays. Abstr Appl Anal 2014:967328

    MathSciNet  MATH  Google Scholar 

  35. Liu X, Ballinger G (2003) Boundedness for impulsive delay differential equations and applications to population growth models. Nonlinear Anal Theory Methods Appl 53(7–8):1041–1062

    MathSciNet  MATH  Google Scholar 

  36. Fullér R (1995) Neural fuzzy systems, Lecture Notes. Abo Akademi University

  37. Lakshmikantham V, Simeonov PS (1989) Theory of impulsive differential equations, vol 6. World Scientific, Singapore

    MATH  Google Scholar 

  38. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I Regul Pap 52(2):417–426

    MathSciNet  MATH  Google Scholar 

  39. Song Q, Zhang J, Maharajan C, Raja R, Cao J, Rajchakit G, Alsaedi A (2018) Impulsive Cohen–Grossberg BAM neural networks with mixed time-delays: an exponential stability analysis issue. Neurocomputing 275:2588–2602

    Google Scholar 

  40. Li Y, Zhao L, Zhang T (2011) Global exponential stability and existence of periodic solution of impulsive Cohen–Grossberg neural networks with distributed delays on time scales. Neural Process Lett 33(1):61–81

    Google Scholar 

  41. Hu M, Wang L (2010) Existence and stability of anti-periodic solutions for an impulsive Cohen–Grossberg sicnns on time scales. Int J Math Comput Sci 6(3):159–165

    Google Scholar 

  42. Şaylı M, Yılmaz E (2015) Periodic solution for state-dependent impulsive shunting inhibitory CNNs with time-varying delays. Neural Netw 68:1–11

    MATH  Google Scholar 

  43. Huang C, Liu B, Tian X, Yang L, Zhang X (2019) Global convergence on asymptotically almost periodic SICNNs with nonlinear decay functions. Neural Process Lett 49(2):625–641

    Google Scholar 

  44. Liang J, Qian H, Liu B (2018) Pseudo almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Neural Process Lett 48(2):1201–1212

    Google Scholar 

  45. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Comput Appl 28(8):2313–2320

    Google Scholar 

  46. Liu Y, Huang Z, Chen L (2012) Almost periodic solution of impulsive Hopfield neural networks with finite distributed delays. Neural Comput Appl 21(5):821–831

    Google Scholar 

  47. Xu CJ (2016) Existence and exponential stability of anti-periodic solution in cellular neural networks with time-varying delays and impulsive effects. Electron J Differ Equ 2016(02):1–14

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Units of Mathematics and Applications UR13ES47, Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, BP W, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & Imen Ben Gharbia

Authors
  1. Chaouki Aouiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Imen Ben Gharbia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chaouki Aouiti.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C., Ben Gharbia, I. Piecewise Pseudo Almost-Periodic Solutions of Impulsive Fuzzy Cellular Neural Networks with Mixed Delays. Neural Process Lett 51, 1201–1225 (2020). https://doi.org/10.1007/s11063-019-10130-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-019-10130-9

Keywords

Mathematics Subject Classification

Search

Navigation