General decay anti-synchronization of multi-weighted coupled neural networks with and without reaction–diffusion terms

Abstract

The network models of multi-weighted coupled neural networks (MWCNNs) and multi-weighted coupled reaction–diffusion neural networks (MWCRDNNs) with and without delayed coupling are presented in this paper, respectively. Firstly, on account of the definitions of \(\psi\)-type stability and \(\psi\)-type function, the concept of decay anti-synchronization is proposed. Then, we investigate the decay anti-synchronization of MWCNNs with and without delayed coupling by designing appropriate nonlinear controllers, and several criteria for ensuring decay anti-synchronization are inferred by means of Lyapunov functional method as well as inequality techniques. Similarly, some conditions for decay anti-synchronization of MWCRDNNs with and without delayed coupling are also, respectively, derived. Lastly, two numerical examples with simulations are given to validate the correctness of these derived results.

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

Fig. 1
Fig. 2

References

  1. 1.

    Abdurahman A (2018) New results on the general decay synchronization of delayed neural networks with general activation functions. Neurocomputing 275:2505–2511

    Article  Google Scholar 

  2. 2.

    An XL, Zhang L, Li YZ, Zhang JG (2014) Synchronization analysis of complex networks with multi-weights and its application in public traffic network. Phys A 412:149–156

    MathSciNet  MATH  Article  Google Scholar 

  3. 3.

    An XL, Zhang L, Zhang JG (2015) Research on urban public traffic network with multi-weights based on single bus transfer junction. Phys A 436:748–755

    MathSciNet  MATH  Article  Google Scholar 

  4. 4.

    Asadia E, Silva MG, Antunes CH, Diasc L, Glicksman L (2014) Multi-objective optimization for building retrofit: a model using genetic algorithm and artificial neural network and an application. Energy Build 81:444–456

    Article  Google Scholar 

  5. 5.

    Cao JD, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172

    MATH  Article  Google Scholar 

  6. 6.

    Gao F, Huang T, Sun JP, Wang J, Hussain A, Yang E (2018) A new algorithm of SAR image target recognition based on improved deep convolutional neural network. Cogn Comput. https://doi.org/10.1007/s12559-018-9563-z

  7. 7.

    Geng X, Zhou ZH, Smith-Miles K (2008) Individual stable space: an approach to face recognition under uncontrolled conditions. IEEE Trans Neural Netw 19:1354–1368

    Article  Google Scholar 

  8. 8.

    Hou J, Huang YL, Ren SY (2019) Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction–diffusion terms. Neurocomputing 330:78–93

    Article  Google Scholar 

  9. 9.

    Huang YL, Qiu SH, Ren SY (2019) Finite-time synchronization and passivity of coupled memristive neural networks. Int J Control. https://doi.org/10.1080/00207179.2019.1566640

  10. 10.

    Huang YL, Qiu SH, Ren SY, Zheng ZW (2018) Fixed-time synchronization of coupled Cohen–Grossberg neural networks with and without parameter uncertainties. Neurocomputing 315:157–168

    Article  Google Scholar 

  11. 11.

    Huang YL, Wang SX, Ren SY (2017) Pinning exponential synchronization and passivity of coupled delayed reaction–diffusion neural networks with and without parametric uncertainties. Int J Control. https://doi.org/10.1080/00207179.2017.1384575

  12. 12.

    Hu C, Jiang HJ, Teng ZD (2010) Impulsive control and synchronization for delayed neural networks with reaction–diffusion terms. IEEE Trans Neural Netw 21:67–81

    Article  Google Scholar 

  13. 13.

    Hu JQ, Cao JD, Alofi A, AL-Mazrooei A, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cogn Neurodyn 9:341–350

    Article  Google Scholar 

  14. 14.

    Hien LV, Phat VN, Trinh H (2015) New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems. Nonlinear Dyn 82:563–575

    MathSciNet  MATH  Article  Google Scholar 

  15. 15.

    Lin SH, Kung SY, Lin LJ (1997) Face recognition/detection by probabilistic decision-based neural network. IEEE Trans Neural Netw 8:114–132

    Article  Google Scholar 

  16. 16.

    Liu D, Zhu S, Sun K (2018) Global anti-synchronization of complex-valued memristive neural networks with time delays. IEEE Trans Cyber. https://doi.org/10.1109/TCYB.2018.2812708

  17. 17.

    Liu YJ, Park JH, Guo BZ, Fang F, Zhou FN (2018) Event-triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities. Int J Robust Nonlin 28:3893–3908

    MATH  Article  Google Scholar 

  18. 18.

    Lu JG (2008) Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with dirichlet boundary conditions. Chaos Solitons Fractals 35:116–125

    MathSciNet  MATH  Article  Google Scholar 

  19. 19.

    Ma CQ, Zhang JF (2012) On formability of linear continuous multi-agent systems. J Syst Sci Complex 25:13–29

    MathSciNet  MATH  Article  Google Scholar 

  20. 20.

    Ma CQ, Zhao WW, Zhao YB (2018) Bipartite consensus of discrete-time double-integrator multi-agent systems with measurement noise. J Syst Sci Complex 31:1525–1540

    MathSciNet  MATH  Article  Google Scholar 

  21. 21.

    Mahmoud EE (2012) Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters. J Frankl Inst 349:1247–1266

    MathSciNet  MATH  Article  Google Scholar 

  22. 22.

    Ma Q, Feng G, Xu SY (2013) Delay-dependent stability criteria for reaction–diffusion neural networks with time-varying delays. IEEE Trans Cyber 43:1913–1920

    Article  Google Scholar 

  23. 23.

    Qi DL, Liu MQ, Qiu MK, Zhang SL (2010) Exponential \({\cal{H}}_\infty\) synchronization of general discrete-time chaotic neural networks with or without time delays. IEEE Trans Neural Netw 21:1358–1365

    Article  Google Scholar 

  24. 24.

    Ren FL, Cao JD (2009) Anti-synchronization of stochastic perturbed delayed chaotic neural networks. Neural Comput Appl 18:515–521

    Article  Google Scholar 

  25. 25.

    Sader M, Abdurahman A, Jiang HJ (2018) General decay synchronization of delayed BAM neural networks via nonlinear feedback control. Appl Math Comput 337:302–314

    MathSciNet  MATH  Google Scholar 

  26. 26.

    Sakthivel R, Vadivel P, Mathiyalaganc K, Arunkumar A, Sivachitra M (2015) Design of state estimator for bidirectional associative memory neural networks with leakage delays. Inf Sci 296:263–274

    MathSciNet  MATH  Article  Google Scholar 

  27. 27.

    Shen H, Huo SC, Cao JD, Huang TW (2019) Generalized state estimation for Markovian coupled networks under round-robin protocol and redundant channels. IEEE Trans Cyber 49:1292–1301

    Article  Google Scholar 

  28. 28.

    Tang Z, Park JH, Feng JW (2018) Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay. IEEE Trans Neural Netw Learn Syst 29:908–919

    Article  Google Scholar 

  29. 29.

    Venetianer PL, Roska T (1998) Image compression by cellular neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 45:205–215

    Article  Google Scholar 

  30. 30.

    Wang H, Duan S, Huang T, Wang L, Li C (2017) Exponential stability of complex-valued memristive recurrent neural networks. IEEE Trans Neural Netw Learn Sys 28:766–771

    Article  Google Scholar 

  31. 31.

    Wang JL, Wu HN (2014) Synchronization and adaptive control of an array of linearly coupled reaction–diffusion neural networks with hybrid coupling. IEEE Trans Cyber 44:1350–1361

    Article  Google Scholar 

  32. 32.

    Wang JL, Wu HN, Guo L (2011) Passivity and stability analysis of reaction–diffusion neural networks with dirichlet boundary conditions. IEEE Trans Neural Netw 22:2105–2116

    Article  Google Scholar 

  33. 33.

    Wang JL, Wu HN, Huang TW, Ren SY (2015) Passivity and synchronization of linearly coupled reaction–diffusion neural networks with adaptive coupling. IEEE Trans Cyber 45:1942–1952

    Article  Google Scholar 

  34. 34.

    Wang JL, Xu M, Wu HN, Huang TW (2018) Finite-time passivity of coupled neural networks with multiple weights. IEEE Trans Netw Sci Eng. 5:184–197

    MathSciNet  Article  Google Scholar 

  35. 35.

    Wang LM, Shen Y, Zhang GD (2016) Synchronization of a class of switched neural networks with time-varying delays via nonlinear feedback control. IEEE Trans Cyber 46:2300–2310

    Article  Google Scholar 

  36. 36.

    Wang LM, Shen Y, Zhang GD (2016) General decay synchronization stability for a class of delayed chaotic neural networks with discontinuous activations. Neurocomputing 179:169–175

    Article  Google Scholar 

  37. 37.

    Wang LM, Zeng ZG, Ge MF, Hu JH (2018) Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays. Neural Netw 105:65–74

    MATH  Article  Google Scholar 

  38. 38.

    Wang Q, Wang JL, Ren SY, Huang YL (2018) Analysis and adaptive control for lag \({\cal{H}}_\infty\) synchronization of coupled reaction–diffusion neural networks. Neurocomputing 319:144–154

    Article  Google Scholar 

  39. 39.

    Wang WP, Li LX, Peng HP, Wang WN, Kurths J, Xiao JH, Yang YX (2016) Anti-synchronization of coupled memristive neutral-type neural networks with mixed time-varying delays via randomly occurring control. Nonlinear Dyn 4:2143–2155

    MathSciNet  MATH  Article  Google Scholar 

  40. 40.

    Wu FG, Hu SG (2012) Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations. Int J Robust Nonlin 22:763–777

    MathSciNet  MATH  Article  Google Scholar 

  41. 41.

    Wu W, Chen TP (2008) Global synchronization criteria of linearly coupled neural network systems with time-varying coupling. IEEE Trans Neural Netw 19:319–332

    Article  Google Scholar 

  42. 42.

    Wu YZ, Liu L, Hu JP, Feng G (2018) Adaptive anti-synchronization of multilayer reaction–diffusion neural networks. IEEE Trans Neural Netw Learn Syst 29:807–818

    MathSciNet  Article  Google Scholar 

  43. 43.

    Yang CB, Huang TZ (2014) Improved stability criteria for a class of neural networks with variable delays and impulsive perturbations. Appl Math Comput 243:923–935

    MathSciNet  MATH  Google Scholar 

  44. 44.

    Yue ZY, Gao F, Xiong QX, Wang J, Huang T, Yang E, Zhou HY (2019) A novel semi-supervised convolutional neural network method for synthetic aperture radar image recognition. Cogn Comput. https://doi.org/10.1007/s12559-019-09639-x

  45. 45.

    Zhang CK, He Y, Jiang L, Wang QG, Wu M (2017) Stability analysis of discrete-time neural networks with time-varying delay via an extended reciprocally convex matrix inequality. IEEE Trans Cyber 47:3040–3049

    Article  Google Scholar 

  46. 46.

    Zhang FH, Zeng ZG (2018) Multiple \(\psi\)-type stability of Cohen–Grossberg neural networks with unbounded time-varying delays. IEEE Trans Syst Man Cyber. https://doi.org/10.1109/TSMC.2018.2876003

  47. 47.

    Zhang RM, Zeng DQ, Park JH, Zhong SM, Yu YB (2018) Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays. J Frankl Inst 355:2826–2848

    MathSciNet  MATH  Article  Google Scholar 

  48. 48.

    Zhang W, Li CD, Huang TW, He X (2015) Synchronization of memristor-based coupling recurrent neural networks with time-varying delays and impulses. IEEE Trans Neural Netw Learn Syst 26:3308–3313

    MathSciNet  Article  Google Scholar 

  49. 49.

    Zhang ZQ, Ren L (2018) New sufficient conditions on global asymptotic synchronization of inertial delayed neural networks by using integrating inequality techniques. Nonlinear Dyn. https://doi.org/10.1007/s11071-018-4603-5

  50. 50.

    Zhang ZQ, Cao JD (2018) Novel finite-time synchronization criteria for inertial neural networks with time delays via integral inequality method. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2018.2868800

  51. 51.

    Zhang ZQ, Li AL, Yu SH (2018) Finite-time synchronization for delayed complex-valued neural networks via integrating inequality method. Neurocomputing 318:248–260

    Article  Google Scholar 

  52. 52.

    Zhao HY, Zhang Q (2011) Global impulsive exponential anti-synchronization of delayed chaotic neural networks. Neurocomputing 74:563–567

    Article  Google Scholar 

  53. 53.

    Zhao YP, He P, Nik HS, Ren J (2015) Robust adaptive synchronization of uncertain complex networks with multiple time-varying coupled delays. Complexity 20:62–73

    MathSciNet  Article  Google Scholar 

  54. 54.

    Zheng MW, Li LX, Peng HP, Xiao JH, Yang YX, Zhang YP, Zhao H (2019) General decay synchronization of complex multi-links time-varying dynamic network. Commun Nonlinear Sci Numer Simul 67:108–123

    MathSciNet  Article  Google Scholar 

  55. 55.

    Zheng ZW, Huang YT, Xie LH, Zhu B (2018) Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output. IEEE Trans Control Syst Technol 26:1851–1859

    Article  Google Scholar 

  56. 56.

    Zheng ZW, Sun L, Xie LH (2018) Error constrained LOS path following of a surface vessel with actuator saturation and faults. IEEE Trans Syst Man Cybern Syst 48:2168–2216

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. They also wish to express their sincere appreciation to Prof. Jinliang Wang for the fruitful discussions and valuable suggestions which helped to improve this paper. This work was supported in part by the Natural Science Foundation of Tianjin City under Grant 18JCQNJC74300, in part by the National Natural Science Foundation of China under Grant 61773285, and in part by Chinese Scholarship Council (No. 201808120044). Dr E. Yang is supported in part under the RSE-NNSFC Joint Project (2017–2019) under Grant 6161101383 with China University of Petroleum (East China).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yanli Huang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Verify currency and authenticity via CrossMark

Cite this article

Huang, Y., Hou, J. & Yang, E. General decay anti-synchronization of multi-weighted coupled neural networks with and without reaction–diffusion terms. Neural Comput & Applic 32, 8417–8430 (2020). https://doi.org/10.1007/s00521-019-04313-7

Download citation

Keywords

  • General decay anti-synchronization
  • MWCNNs
  • Nonlinear control
  • Delayed coupling
  • Reaction–diffusion terms