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Exponential Synchronization of Inertial Memristor-Based Neural Networks with Time Delay Using Average Impulsive Interval Approach

  • R. Rakkiyappan
  • D. Gayathri
  • G. Velmurugan
  • Jinde CaoEmail author
Article
  • 42 Downloads

Abstract

This paper deals with the impulsive synchronization problem for a class of inertial memristor-based neural networks (IMNNs) with time delays by applying average impulsive interval approach. By adopting proper variable transformation, the original system can be converted into first-order differential equations. By utilizing Lyapunov theory, theory of differential inclusion, Halanay inequality and average impulsive interval approach, we attain some adequate conditions that make sure the exponential synchronization of IMNNs under the impulsive control technique. Moreover some delay-dependent conditions for delayed impulsive synchronization of the considered system is obtained. Finally, numerical simulations are offered to exhibit the capacity of our theoretical findings.

Keywords

Synchronization Inertial memristor-based neural networks Average impulsive interval approach Impulsive controller 

Notes

References

  1. 1.
    Chen C, Li L, Peng H, Yang Y, Li T (2017) Finite-time synchronization of memristor-based neural networks with mixed delays. Neurocomputing 235:83–89CrossRefGoogle Scholar
  2. 2.
    Hu J, Zeng C (2017) Adaptive exponential synchronization of complex-valued Cohen–Grossberg neural networks with known and unknown parameters. Neural Netw 86:90–101CrossRefGoogle Scholar
  3. 3.
    Wu Y, Cao J, Li Q, Alshaedi A, Alshaadi FE (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139CrossRefGoogle Scholar
  4. 4.
    Cao Y, Samidurai R, Sriraman R (2019) Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function. Math Comput Simul 155:57–77MathSciNetCrossRefGoogle Scholar
  5. 5.
    Guo Z, Wang J, Yan Z (2015) Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling. IEEE Trans Syst Man Cybern B Cybern 45:235–249CrossRefGoogle Scholar
  6. 6.
    Chua LO (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRefGoogle Scholar
  7. 7.
    Zhang W, Li C, Huang T, Huang J (2016) Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control. Neurocomputing 173:1066–1072CrossRefGoogle Scholar
  8. 8.
    Bao H, Park JH, Cao J (2015) Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays. Appl Math Comput 270:543–556MathSciNetGoogle Scholar
  9. 9.
    Liu D, Zhu S, Chang W (2017) Input-to-state stability of memristor-based complex-valued neural networks with time delays. Neurocomputing 221:159–167CrossRefGoogle Scholar
  10. 10.
    Rakkiyappan R, Sivaranjani K, Velmurugan G (2014) Passivity and passification of memristor-based complex-valued recurrent neural networks with interval time-varying delays. Neurocomputing 144:391–417CrossRefGoogle Scholar
  11. 11.
    Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhao H (2016) Finite-time stability and synchronization for memristor-based fractional-order Cohen–Grossberg neural network. Eur Phys J B 89:204MathSciNetCrossRefGoogle Scholar
  12. 12.
    Shi Y, Cao J, Chen G (2017) Exponential stability of complex-valued memristor-based neural networks with time-varying delays. Appl Math Comput 313:222–234MathSciNetGoogle Scholar
  13. 13.
    Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhang Y, Zhao H (2018) Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks. Commun Nonlinear Sci Numer Simul 59:272–291MathSciNetCrossRefGoogle Scholar
  14. 14.
    Chen C, Li L, Peng H, Yang Y (2017) Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay. Neural Netw 96:47–54CrossRefGoogle Scholar
  15. 15.
    Chen C, Li L, Peng H, Yang Y (2018) Adaptive synchronization of memristor-based BAM neural networks with mixed delays. Appl Math Comput 322:100–110MathSciNetGoogle Scholar
  16. 16.
    Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172CrossRefzbMATHGoogle Scholar
  17. 17.
    Ke YQ, Miao CF (2013) Stability and existence of periodic solutions in inertial BAM neural networks with time-delays. Neural Comput Appl 23:1089–1099CrossRefGoogle Scholar
  18. 18.
    Ke YQ, Miao CF (2013) Stability analysis of inertial Cohen–Grossberg-type neural networks with time delays. Neurocomputing 117:196–205CrossRefGoogle Scholar
  19. 19.
    Zhang ZQ, Quan ZY (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151:1316–1326CrossRefGoogle Scholar
  20. 20.
    Qi JQ, Li CD, Huang TW (2015) Stability of inertial BAM neural network with time varying delay via impulsive control. Neurocomputing 161:162–167CrossRefGoogle Scholar
  21. 21.
    Dharani S, Rakkiyappan R, Park JH (2017) Pinning sampled-data synchronization of coupled inertial neural networks with reaction-diffusion terms and time-varying delays. Neurocomputing 227:101–107CrossRefGoogle Scholar
  22. 22.
    Hu J, Cao J, Alofi A, AL-Mazrooei A, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cognit Neurodyn 9:341–350CrossRefGoogle Scholar
  23. 23.
    Rakkiyappan R, Udhaya Kumari E, Chandrasekar A, Krishnasamy R (2016) Synchronization and periodicity of coupled inertial memristive neural networks with supremums. Neurocomputing 214:739–749CrossRefGoogle Scholar
  24. 24.
    Rakkiyappan R, Premalatha S, Chandrasekar A, Cao J (2016) Stability and synchronization analysis of inertial memristive neural networks with time delays. Cognit Neurodyn 10:437–451CrossRefGoogle Scholar
  25. 25.
    He W, Qian F, Cao J (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Netw 85:1–9CrossRefGoogle Scholar
  26. 26.
    Cao Y, Zhang L, Li C, Chen MZQ (2017) Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology. IEEE Trans Cybern 47:2212–2222CrossRefGoogle Scholar
  27. 27.
    Yao F, Cao J, Cheng P, Qiu L (2016) Generalized average dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems. Nonlinear Anal Hybrid Syst 22:147–160MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Pan L, Cao J (2012) Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method. Adv Differ Eqn 2012:61Google Scholar
  29. 29.
    Chen W, Luo S, Zheng WX (2017) Generating globally stable periodic solutions of delayed neural networks with periodic coefficients via impulsive control. IEEE Trans Cybern 47:1590–1603CrossRefGoogle Scholar
  30. 30.
    Li X, Bohner M, Wang C (2015) Impulsive differential equations: periodic solutions and applications. Automatica 52:173–178MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Li X, Ho D, Cao J (2019) Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica 99:361–368MathSciNetCrossRefGoogle Scholar
  32. 32.
    Zhang W, Li C, Huang T, Qi J (2014) Global exponential synchronization for coupled switched delayed recurrent neural networks with stochastic perturbation and impulsive effects. Neural Comput Appl 25:1275–1283CrossRefGoogle Scholar
  33. 33.
    Yang X, Cao J, Qiu J (2015) \(p\)th moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91CrossRefzbMATHGoogle Scholar
  34. 34.
    Cai S, Li X, Jia Q, Liu Z (2016) Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks:average impulsive interval approach. Nonlinear Dyn 85:1–19CrossRefzbMATHGoogle Scholar
  35. 35.
    Benchohra M, Hamani S, Nieto JJ (2010) The method of upper and lower solutions for second order differential inclusions with integral boundary conditions. J Math 40:13–26MathSciNetzbMATHGoogle Scholar
  36. 36.
    Yang Z, Xu D (2007) Stability analysis and design of impulsive control systems with time delay. IEEE Trans Autom Control 52:1448–1454MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Halanay A (1966) Differential equations: stability, oscillations, time lags, vol 23. Academic Press, New YorkzbMATHGoogle Scholar
  38. 38.
    Boyd S, El Ghaoui L, Eric F, Balakrishnan V (1997) Linear matrix inequalities in system and control theory. Society for Industrial Mathematics, PhiladelphiazbMATHGoogle Scholar
  39. 39.
    Chen J, Zeng Z, Jiang P (2014) Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8CrossRefzbMATHGoogle Scholar
  40. 40.
    Lakshmanan S, Lim CP, Prakash M, Nahavandi S, Balasubramaniam P (2017) Neutral-type of delayed inertial neural networks and their stability analysis using the LMI Approach. Neurocomputing 230:243–250CrossRefGoogle Scholar
  41. 41.
    Zhang W, Huang TW, He X, Li CD (2017) Global exponential stability of inertial memristor-based neural networks with time-varying delayed and impulses. Neural Netw 95:102–109CrossRefGoogle Scholar
  42. 42.
    Chua L (2011) Resistance switching memories are memristor. Appl Phys A 102:765–783CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • R. Rakkiyappan
    • 1
  • D. Gayathri
    • 1
  • G. Velmurugan
    • 1
  • Jinde Cao
    • 2
    Email author
  1. 1.Department of MathematicsBharathiar UniversityCoimbatoreIndia
  2. 2.School of Mathematics and Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjingChina

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