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Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays

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Abstract

This paper considers the global exponential stability (GES) of high-order bidirectional associative memory (BAM) neural networks with proportional delays. Here, proportional delays are unbounded time-varying delays, which are different from constant delays, bounded time-varying delays and distributed delays. Through variable transformations, the original system can be transformed equivalently into high-order BAM neural networks with multi-constant delays and time-varying coefficients. By utilizing Brouwer’s fixed point theorem and constructing appropriate delay differential inequalities, new sufficient criteria are established to guarantee the existence, uniqueness and GES of the equilibrium point for the considered model. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of the proposed results.

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References

  1. Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26(23):4947–4960

    Article  Google Scholar 

  2. Kosko B (1988) Bidirectional associative memories. IEEE Trans Syst Man Cybern 18(1):49–60

    Article  MathSciNet  Google Scholar 

  3. Xiao J et al (2017) Finite-time Mittag–Leffler synchronization of fractional-order memristive BAM neural networks with time delays. Neurocomputing 219:431–439

    Article  Google Scholar 

  4. Ren L, Yi X, Zhang Z (2019) Global asymptotic stability of periodic solutions for discrete time delayed BAM neural networks by combining coincidence degree theory with LMI method. Neural Process Lett 50:1321–1340

    Article  Google Scholar 

  5. Jian J, Wang B (2015) Stability analysis in Lagrange sense for a class of BAM neural networks of neutral type with multiple time-varying delays. Neurocomputing 149:930–939

    Article  Google Scholar 

  6. Wen Z, Sun J (2008) Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis. Neurocomputing 71(7–9):1543–1549

    Article  Google Scholar 

  7. Li Y, Gao S (2010) Global exponential stability for impulsive BAM neural networks with distributed delays on time scales. Neural Process Lett 31(1):65–91

    Article  Google Scholar 

  8. Liu X-G et al (2008) Global exponential stability of bidirectional associative memory neural networks with time delays. IEEE Trans Neural Netw 19(3):397–407

    Article  Google Scholar 

  9. Zhou H, Zhou Z, Jiang W (2015) Almost periodic solutions for neutral type BAM neural networks with distributed leakage delays on time scales. Neurocomputing 157:223–230

    Article  Google Scholar 

  10. Chen A, Cao J, Huang L (2004) Exponential stability of BAM neural networks with transmission delays. Neurocomputing 57:435–454

    Article  Google Scholar 

  11. Liu B, Huang L (2006) Global exponential stability of BAM neural networks with recent-history distributed delays and impulses. Neurocomputing 69(16-18):2090–2096

    Article  Google Scholar 

  12. Zhang Z, Quan Z (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151:1316–1326

    Article  Google Scholar 

  13. Lou X, Cui B (2006) On the global robust asymptotic stability of BAM neural networks with time-varying delays. Neurocomputing 70(1-3):273–279

    Article  Google Scholar 

  14. Li X (2009) Exponential stability of Cohen–Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 73(1–3):525–530

    Article  Google Scholar 

  15. Liu J, Zong G (2009) New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type. Neurocomputing 72(10-12):2549–2555

    Article  Google Scholar 

  16. Zhang Z, Liu K, Yang Y (2012) New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type. Neurocomputing 81:24–32

    Article  Google Scholar 

  17. 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

    Article  Google Scholar 

  18. Liu Y, Wang Z, Liu X (2009) On global stability of delayed BAM stochastic neural networks with Markovian switching. Neural Process Lett 30(1):19–35

    Article  Google Scholar 

  19. Liu C, Li C, Liao X (2011) Variable-time impulses in BAM neural networks with delays. Neurocomputing 74(17):3286–3295

    Article  Google Scholar 

  20. Zhu Q, Rakkiyappan R, Chandrasekar A (2014) Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control. Neurocomputing 136:136–151

    Article  Google Scholar 

  21. Bao H (2016) Existence and exponential stability of periodic solution for BAM fuzzy Cohen–Grossberg neural networks with mixed delays. Neural Process Lett 43(3):871–885

    Article  Google Scholar 

  22. Cao J, Wang L (2002) Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw 13(2):457–463

    Article  Google Scholar 

  23. Abu-Mostafa YASER, St Jacques J (1985) Information capacity of the Hopfield model. IEEE Trans Inf Theory 31(4):461–464

    Article  MATH  Google Scholar 

  24. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554–2558

    Article  MathSciNet  MATH  Google Scholar 

  25. Simpson PK (1990) Higher-ordered and intraconnected bidirectional associative memories. IEEE Trans Syst Man Cybern 20(3):637–653

    Article  Google Scholar 

  26. 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 

  27. Huo H-F, Li W-T, Tang S (2009) Dynamics of high-order BAM neural networks with and without impulses. Appl Math Comput 215(6):2120–2133

    MathSciNet  MATH  Google Scholar 

  28. Qiu J, Cao J (2005) An analysis for periodic solutions of high-order BAM neural networks with delays. International symposium on neural networks. Springer, Berlin

  29. Wang F, Liu M (2016) Global exponential stability of high-order bidirectional associative memory (BAM) neural networks with time delays in leakage terms. Neurocomputing 177:515–528

    Article  Google Scholar 

  30. Aouiti C, Li X, Miaadi F (2019) A new LMI approach to finite and fixed time stabilization of high-order class of BAM neural networks with time-varying delays. Neural Process Lett 50:815–838

  31. Ho DWC, Liang J, Lam J (2006) Global exponential stability of impulsive high-order BAM neural networks with time-varying delays. Neural Netw 19(10):1581–1590

    Article  MATH  Google Scholar 

  32. Gu H (2011) Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays. Neurocomputing 74(5):720–729

    Article  Google Scholar 

  33. Guo Y, Xin L (2018) Asymptotic and robust mean square stability analysis of impulsive high-order BAM neural networks with time-varying delays. Circuits Syst Signal Process 37(7):2805–2823

    Article  MathSciNet  MATH  Google Scholar 

  34. Yang W, Wenwu Y, Cao J (2018) Global exponential stability of impulsive fuzzy high-order bam neural networks with continuously distributed delays. IEEE Trans Neural Netw Learn Syst 29(8):3682–3700

    Article  MathSciNet  Google Scholar 

  35. Yang C-B, Huang T-Z, Shao J-L (2013) New results for periodic solution of high-order BAM neural networks with continuously distributed delays and impulses. J Appl Math 2013:247046

  36. Zhou L (2013) Delay-dependent exponential stability of cellular neural networks with multi-proportional delays. Neural Process Lett 38(3):347–359

    Article  Google Scholar 

  37. Zhou L (2018) Delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays. Neurocomputing 308:235–244

    Article  Google Scholar 

  38. Jia S et al (2018) Asymptotical and adaptive synchronization of Cohen–Grossberg neural networks with heterogeneous proportional delays. Neurocomputing 275:1449–1455

    Article  Google Scholar 

  39. Zhang A (2018) Almost periodic solutions for SICNNs with neutral type proportional delays and D operators. Neural Process Lett 47(1):57–70

    Article  Google Scholar 

  40. Su L, Zhou L (2017) Passivity of memristor-based recurrent neural networks with multi-proportional delays. Neurocomputing 266:485–493

    Article  Google Scholar 

  41. Zheng C, Li N, Cao J (2015) Matrix measure based stability criteria for high-order neural networks with proportional delay. Neurocomputing 149:1149–1154

    Article  Google Scholar 

  42. Cui N et al (2018) Global asymptotic and robust stability of inertial neural networks with proportional delays. Neurocomputing 272:326–333

    Article  Google Scholar 

  43. Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161:99–106

    Article  Google Scholar 

  44. Xu C, Li P, Pang Y (2016) Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays. Math Methods Appl Sci 39(18):5720–5731

    Article  MathSciNet  MATH  Google Scholar 

  45. Yang G (2019) Exponential stability of positive recurrent neural networks with multi-proportional delays. Neural Process Lett 49:67–78

  46. Zhou L, Liu X (2017) Mean-square exponential input-to-state stability of stochastic recurrent neural networks with multi-proportional delays. Neurocomputing 219:396–403

    Article  Google Scholar 

  47. Liu B (2017) Finite-time stability of a class of CNNs with heterogeneous proportional delays and oscillating leakage coefficients. Neural Process Lett 45(1):109–119

    Article  Google Scholar 

  48. Song Q et al (2018) Dynamics of complex-valued neural networks with variable coefficients and proportional delays. Neurocomputing 275:2762–2768

    Article  Google Scholar 

  49. Guan K, Yang J (2019) Global asymptotic stabilization of cellular neural networks with proportional delay via impulsive control. Neural Process Lett 50(2):1969–1992

    Article  Google Scholar 

  50. Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355

    Article  Google Scholar 

  51. Wang W et al (2016) Anti-synchronization control of memristive neural networks with multiple proportional delays. Neural Process Lett 43(1):269–283

    Article  Google Scholar 

  52. Yu Y (2017) Exponential stability of pseudo almost periodic solutions for cellular neural networks with multi-proportional delays. Neural Process Lett 45(1):141–151

    Article  Google Scholar 

  53. Kulkarni S, Sharma R, Mishra I (2012) New QoS routing algorithm for MPLS networks using delay and bandwidth constraints. Int J Inf Commun Technol 2:285–293

    Google Scholar 

Download references

Acknowledgements

The research of Z. X. Yu was partially supported by Natural Science Foundation of Shanghai (No. 18ZR1426500). The authors thank the referees and the Editor-in-Chief for their valuable comments and suggestions that help the improvement of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Jiacheng Zu & Zhixian Yu

  2. Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Jiacheng Zu

  3. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Yanling Meng

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  1. Jiacheng Zu
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  2. Zhixian Yu
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  3. Yanling Meng
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Correspondence to Zhixian Yu.

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Zu, J., Yu, Z. & Meng, Y. Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays. Neural Process Lett 51, 2531–2549 (2020). https://doi.org/10.1007/s11063-020-10206-x

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