Skip to main content
SpringerLink
Log in

Finite-time synchronization of complex-valued neural networks with reaction-diffusion terms: an adaptive intermittent control approach

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, we present a novel approach to achieve finite-time synchronization (FTS) in a certain class of fractional-order complex-valued neural networks (CVNNs) containing reaction-diffusion terms. The proposed method uses intermittent control and provides a theoretical analysis to establish criteria for achieving FTS. This is achieved through new Lyapunov functions based on the proposed system, deriving inequalities in the complex domain. To realize FTS, the study designs complex-valued intermittent controllers for the targeted CVNNs relying solely on the information obtained from the controlled nodes. Moreover, an adaptive controller is introduced to effectively regulate the control gain, and the FTS of CVNNs is analyzed. The effectiveness of the proposed control strategies and derived results is demonstrated by numerical examples.

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
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

References

  1. Song J, Niu Y, Zou Y (2016) Finite-time sliding mode control synthesis under explicit output constraint. Automatica 65:111–114

    MathSciNet  Google Scholar 

  2. Hernandez-Gonzalez M, Hernandez-Vargas EA, Basin MV (2018) Discrete-time high order neural network identifier trained with cubature kalman filter. Neurocomputing 322:13–21

    Google Scholar 

  3. Ali MS, Saravanan S, Arik S (2016) Finite-time \({H}_\infty \) state estimation for switched neural networks with time-varying delays. Neurocomputing 207:580–589

    Google Scholar 

  4. Ali MS, Saravanan S, Palanisamy L (2019) Stochastic finite-time stability of reaction-diffusion cohen-grossberg neural networks with time-varying delays. Chinese J Phys 57:314–328

    ADS  Google Scholar 

  5. Kan Y, Lu J, Qiu J, Kurths J (2019) Exponential synchronization of time-varying delayed complex-valued neural networks under hybrid impulsive controllers. Neural Netw 114:157–163

    PubMed  Google Scholar 

  6. Yan S, Gu Z, Park JH, Xie X. Synchronization of delayed fuzzy neural networks with probabilistic communication delay and its application to image encryption, IEEE Transactions on Fuzzy Systems (2022)

  7. Long C, Zhang G, Zeng Z, Hu J (2022) Finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms: a non-separation approach. Neural Netw 148:86–95

    PubMed  Google Scholar 

  8. Arena P, Fortuna L, Porto D (2000) Chaotic behavior in noninteger-order cellular neural networks. Phys RevE 61(1):776

    ADS  CAS  Google Scholar 

  9. Bao H, Park JH, Cao J (2016) Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 81:16–28

    PubMed  Google Scholar 

  10. Wu A, Zeng Z (2016) Boundedness, mittag-leffler stability and asymptotical \(\omega \)-periodicity of fractional-order fuzzy neural networks. Neural Netw 74:73–84

    PubMed  Google Scholar 

  11. Chen J, Zeng Z, Jiang P (2014) Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8

    PubMed  Google Scholar 

  12. Yuan Y, Song Q, Liu Y, Alsaadi FE (2019) Synchronization of complex-valued neural networks with mixed two additive time-varying delays. Neurocomputing 332:149–158

    Google Scholar 

  13. Yang S, Yu J, Hu C, Jiang H (2018) Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks. Neural Netw 104:104–113

    PubMed  Google Scholar 

  14. Song Q, Zhao Z (2016) Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 171:179–184

    Google Scholar 

  15. Song X, Li X, Song S, Zhang Y, Ning Z (2021) Quasi-synchronization of coupled neural networks with reaction-diffusion terms driven by fractional brownian motion. J Franklin Inst 358(4):2482–2499

    MathSciNet  Google Scholar 

  16. Kondo S, Miura T (2010) Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329(5999):1616–1620

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  17. Adamatzky A, Arena P, Basile A, Carmona-Galán R, Costello BDL, Fortuna L, Frasca M, Rodríguez-Vázquez A (2004) Reaction-diffusion navigation robot control: from chemical to vlsi analogic processors. IEEE Trans Circuits Syst I: Regular Papers 51(5):926–938

    Google Scholar 

  18. Wei T, Lin P, Zhu Q, Wang L, Wang Y (2018) Dynamical behavior of nonautonomous stochastic reaction-diffusion neural-network models. IEEE Trans Neural Netw Learn Syst 30(5):1575–1580

    MathSciNet  PubMed  Google Scholar 

  19. Sun L, Wang J, Chen X, Shi K, Shen H (2021) \(h_\infty \) fuzzy state estimation for delayed genetic regulatory networks with random gain fluctuations and reaction-diffusion. J Franklin Inst 358(16):8694–8714

    MathSciNet  Google Scholar 

  20. Alqudah MA, Ashraf R, Rashid S, Singh J, Hammouch Z, Abdeljawad T (2021) Novel numerical investigations of fuzzy cauchy reaction-diffusion models via generalized fuzzy fractional derivative operators. Fractal Fract 5(4):151

    Google Scholar 

  21. Cao Y, Cao Y, Guo Z, Huang T, Wen S (2020) Global exponential synchronization of delayed memristive neural networks with reaction-diffusion terms. Neural Netw 123:70–81

    PubMed  Google Scholar 

  22. Wei T, Li X, Stojanovic V (2021) Input-to-state stability of impulsive reaction-diffusion neural networks with infinite distributed delays. Nonlinear Dyn 103:1733–1755

    Google Scholar 

  23. Shabunin A, Astakhov V, Demidov V, Provata A, Baras F, Nicolis G, Anishchenko V (2003) Modeling chemical reactions by forced limit-cycle oscillator: synchronization phenomena and transition to chaos. Chaos, Solitons & Fractals 15(2):395–405

    ADS  Google Scholar 

  24. Lestienne R (2001) Spike timing, synchronization and information processing on the sensory side of the central nervous system. Prog Neurobiol 65(6):545–591

    CAS  PubMed  Google Scholar 

  25. Yang T, Chua LO (1997) Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans Circuits Syst I: Fundam Theory Appl 44(10):976–988

    MathSciNet  Google Scholar 

  26. Yang X, Cao J (2013) Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans Circuits Syst I: Regular Papers 60(9):2431–2439

    MathSciNet  Google Scholar 

  27. Sun W, Wang S, Wang G, Wu Y (2015) Lag synchronization via pinning control between two coupled networks. Nonlinear Dyn 79:2659–2666

    MathSciNet  Google Scholar 

  28. Pecora LM, Sorrentino F, Hagerstrom AM, Murphy TE, Roy R (2014) Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nat Commun 5(1):4079

    ADS  CAS  PubMed  Google Scholar 

  29. Palva S, Palva JM (2011) Functional roles of alpha-band phase synchronization in local and large-scale cortical networks. Front Psychol 2:204

    PubMed  PubMed Central  Google Scholar 

  30. Li H-L, Cao J, Jiang H, Alsaedi A (2018) Graph theory-based finite-time synchronization of fractional-order complex dynamical networks. J Franklin Inst 355(13):5771–5789

    MathSciNet  Google Scholar 

  31. Luo T, Wang Q, Jia Q, Xu Y (2022) Asymptotic and finite-time synchronization of fractional-order multiplex networks with time delays by adaptive and impulsive control. Neurocomputing 493:445–461

    Google Scholar 

  32. Stamova I, Stamov G (2017) Mittag-leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers. Neural Netw 96:22–32

    PubMed  Google Scholar 

  33. Zhang L, Zhong J, Lu J (2021) Intermittent control for finite-time synchronization of fractional-order complex networks. Neural Netw 144:11–20

    PubMed  Google Scholar 

  34. Cai S, Hou M (2021) Quasi-synchronization of fractional-order heterogeneous dynamical networks via aperiodic intermittent pinning control. Chaos, Solitons & Fractals 146:110901

    MathSciNet  Google Scholar 

  35. Zhao L (2021) A note on cluster synchronization of fractional-order directed networks via intermittent pinning control. Physica A: Stat Mech Appl 561:125150

    ADS  MathSciNet  Google Scholar 

  36. Wang Y, Wu Z (2021) Cluster synchronization in variable-order fractional community network via intermittent control. Mathematics 9(20):2596

    Google Scholar 

  37. Lu X, Zhang X, Liu Q (2018) Finite-time synchronization of nonlinear complex dynamical networks on time scales via pinning impulsive control. Neurocomputing 275:2104–2110

    Google Scholar 

  38. Song X, Man J, Song S, Zhang Y, Ning Z (2020) Finite/fixed-time synchronization for markovian complex-valued memristive neural networks with reaction-diffusion terms and its application. Neurocomputing 414:131–142

    Google Scholar 

  39. Li X, Fang J-A, Zhang W, Li H (2018) Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions. Neurocomputing 316:284–293

    Google Scholar 

  40. Narayanan G, Muhiuddin G, Ali MS, Diab AAZ, Al-Amri JF, Abdul-Ghaffar H (2022) Impulsive synchronization control mechanism for fractional-order complex-valued reaction-diffusion systems with sampled-data control: Its application to image encryption. IEEE Access 10:83620–83635

    Google Scholar 

  41. Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier

  42. Gan Q (2013) Exponential synchronization of stochastic fuzzy cellular neural networks with reaction-diffusion terms via periodically intermittent control. Neural Process Lett 37(3):393–410

    Google Scholar 

  43. Palanivel J, Suresh K, Premraj D, Thamilmaran K (2018) Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator. Chaos, Solitons & Fractals 106:35–43

    ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge this work is funded by the Centre for Nonlinear Systems, Chennai Institute of Technology (CIT), India, vide funding number CIT/CNS/2024/RP-005.

Author information

Authors and Affiliations

  1. Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, 600069, India

    Saravanan Shanmugam & Karthikeyan Rajagopal

  2. School of IT Information and Control Engineering, Kunsan National University, Gunsan-si, South Korea

    G. Narayanan

  3. Department of Electronics and Communications Engineering, University Centre for Research and Development, Chandigarh University, Mohali, Punjab, 140 413, India

    Karthikeyan Rajagopal

  4. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, 632 115, India

    M. Syed Ali

Authors
  1. Saravanan Shanmugam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Narayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karthikeyan Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Syed Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

SS and GN contributed to conceptualization, methodology, and writing-original draft; KR helped in formal analysis; KR and MSA done investigation and writing-review & editing; GN done software; SS and MSA done validation; SS contributed to visualization. All authors have read and agreed to the published version of the manuscript

Corresponding author

Correspondence to Karthikeyan Rajagopal.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest regarding the publication of this paper.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shanmugam, S., Narayanan, G., Rajagopal, K. et al. Finite-time synchronization of complex-valued neural networks with reaction-diffusion terms: an adaptive intermittent control approach. Neural Comput & Applic 36, 7389–7404 (2024). https://doi.org/10.1007/s00521-024-09467-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-024-09467-7

Keywords

Search

Navigation