Skip to main content
SpringerLink
Log in

Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper is concerned with the problem of asymptotic stability of neutral type Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional (LKF), reciprocal convex technique and Jensen’s inequality are used to delay-dependent conditions are established to analysis the asymptotic stability of Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Finally numerical examples are given to illustrate the usefulness of our proposed method.

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

Similar content being viewed by others

References

  1. Cohen M, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 3:815–826

    Article  MathSciNet  MATH  Google Scholar 

  2. Wu B, Liu Y, Lu J (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Model 55:837–843

    Article  MathSciNet  MATH  Google Scholar 

  3. Hua H, Liu Y, Lu J, Zhu J (2013) A new impulsive synchronization criterion for T–S fuzzy model and its applications. Appl Math Model 37:8826–8835

    Article  MathSciNet  Google Scholar 

  4. Yang X (2014) Can neural networks with arbitrary delays be finite-timely synchronized? Neurocomputing 143:275–281

    Article  Google Scholar 

  5. Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60:032201

  6. Yang X, Cao J, Qiu J (2015) pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw. 65:80–91

    Article  Google Scholar 

  7. Yang X, Cao J, Yu W (2014) Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays. Cogn Neurodyn 8:239–249

    Article  Google Scholar 

  8. Yang X, Cao J, Ho DWC (2014) Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Cogn Neurodyn 9:113–128

    Article  Google Scholar 

  9. Yang X, Ho DWC (2016) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Syst Man Cybern 46:3377–3387

    Google Scholar 

  10. Yang R, Wu B, Liu Y (2015) A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays. Appl Math Comput 265:696–707

    MathSciNet  Google Scholar 

  11. Liu Y, Zhang D, Lu J, Cao J (2016) Global \(\mu \)-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inf Sci 360:273–288

    Article  Google Scholar 

  12. Song Q, Zhao Z, Liu Y (2016) Dynamics of new class of hopfield neural networks with time-varying and distributed delays. Acta Math Sci 36:891–912

    Article  MathSciNet  Google Scholar 

  13. Zhong S, Li C, Liao X (2010) Global stability of discrete-time Cohen–Grossberg neural networks with impulses. Neurocomputing 73:3132–3138

    Article  Google Scholar 

  14. Liang T, Yang Y, Liu Y, Li L (2014) Exestence and global exponential stability of almost periodic sol to Cohen–Grossberg neural networks with discrete delay on time scales. Neurocomputing 123:207–215

    Article  Google Scholar 

  15. Wang L (2005) Stability of Cohen–Grossberg neural networks with distributed delays. Appl Math Comput 160:93–110

    MathSciNet  MATH  Google Scholar 

  16. Zhu Q, Cao J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21:1314–1325

    Article  Google Scholar 

  17. Chen P, Hiang C, Liang X (2010) Stochastic stability of Cohen–Grossberg neural networks with unbounded distributed delays. Electron J Differ Equ 42:1–11

    MathSciNet  Google Scholar 

  18. Chen Z, Zhad D, Ruan J (2007) Dynamic analysis of high-order Cohen–Grossberg neural networks with time delay. Chaos Solitons Fractals 32:1538–1546

    Article  MathSciNet  MATH  Google Scholar 

  19. Balasubramaniam P, Ali MS (2010) Robust exponential stability of uncertain fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 161:608–618

    Article  MathSciNet  MATH  Google Scholar 

  20. Jian J, Wang B (2015) Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays. Appl Math Comput 116:125

    MathSciNet  Google Scholar 

  21. Kosko B (1992) Neural networks and fuzzy systems a dynamical systems approach to machine intelligence. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  25. Balasubramaniam P, Ali MS (2011) Stability analysis of Takagi–Sugeno fuzzy Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. Math Comput Model 53:151–160

    Article  MathSciNet  MATH  Google Scholar 

  26. Jian J, Wang B (2015) Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays. Math Comput Simul 116:1–25

    Article  MathSciNet  Google Scholar 

  27. Zhang Z, Liu W, Zhou D (2012) Global asymptotic stability to a generalized Cohen–Grossberg BAM neural networks of neutral type delays. Neural Netw 25:94–105

    Article  MATH  Google Scholar 

  28. Du Y, Zhong S, Zhou N, Shi K, Cheng J (2014) Exponential stability for stochastic Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. Neurocomputing 127:144–151

    Article  Google Scholar 

  29. Du Y, Zhong S, Zhou N (2014) Global asymptotic stability of Markovian jumping stochastic Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. Appl Math Comput 243:624–636

    MathSciNet  MATH  Google Scholar 

  30. Kwon OM, Park JH, Lee SM (2008) On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays. Appl Math Comput 197:864–873

    MathSciNet  MATH  Google Scholar 

  31. Li Y, Zhao L, Chen X (2012) Existence of periodic solutions for neutral type cellular neural networks with delays. Appl Math Model 36:1173–1183

    Article  MathSciNet  MATH  Google Scholar 

  32. Shi K, Zhu H, Zhong S, Zeng Y, Zhang Y, Wang W (2015) Stability analysis of neutral type neural networks with mixed time-varying delays using triple-integral and delay-partitioning methods. ISA Trans 58:85–95

    Article  Google Scholar 

  33. Peng W, Wu Q, Zhang Z (2016) LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique. Neurocomputing 199:103–113

    Article  Google Scholar 

  34. Feng J, Xu SY, Zou Y (2009) Delay-dependent stability of neutral type neural networks with distributed delay. Neurocomputing 72:2576–2580

    Article  Google Scholar 

  35. Ali MS, Saravanakumar R, Cao J (2016) New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays. Neurocomputing 171:1533–1547

    Article  Google Scholar 

  36. Li X, Fu X (2011) Global asymptotic stability of stochastic Cohen–Grossberg-type BAM neural networks with mixed delays: an LMI approach. J Comput Appl Math 235:3385–3394

    Article  MathSciNet  MATH  Google Scholar 

  37. Ali MS, Balasubramaniam P (2009) Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays. Expert Syst Appl 36:10583–10588

    Article  Google Scholar 

  38. Zhang Z, Liu W, Zhou D (2012) Global asymptotic stability to a generalized Cohen–Grossberg BAM neural networks of neutral type delays. Neural Netw 25:94–105

    Article  MATH  Google Scholar 

  39. Wang D, Huang L, Cai Z (2013) On the periodic dynamics of a general Cohen–Grossberg BAM neural networks via differential inclusions. Neurocomputing 118:203–214

    Article  Google Scholar 

  40. Sakthivel R, Arunkumar A, Mathiyalagan K (2011) Robust passivity analysis of fuzzy Cohen–Grossberg BAM neural networks with time-varying delays. Appl Math Comput 218:3799–3809

    MathSciNet  MATH  Google Scholar 

  41. Park P, Ko JW, Jeong C (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47:235–238

    Article  MathSciNet  MATH  Google Scholar 

  42. Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in systems and control theory. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  43. Gu K, Kharitonov VL, Chen J (2003) Stability of time delay systems. Birkhuser, Boston

    Book  MATH  Google Scholar 

  44. Liu H, Ou Y, Hu J, Liu T (2010) Delay-depent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters. Neural Netw 23:315–321

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, India

    M. Syed Ali, S. Saravanan, M. Esther Rani & S. Elakkia

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jinde Cao & Tasawar Hayat

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi

  5. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    Tasawar Hayat

Authors
  1. M. Syed Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Saravanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Esther Rani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Elakkia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Tasawar Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinde Cao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ali, M.S., Saravanan, S., Rani, M.E. et al. Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays. Neural Process Lett 46, 991–1007 (2017). https://doi.org/10.1007/s11063-017-9622-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-017-9622-6

Keywords

Search

Navigation