Skip to main content
SpringerLink
Log in

Bipartite Synchronization Analysis of Fractional Order Coupled Neural Networks with Hybrid Control

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

The bipartite synchronization problem for fractional order antagonistic coupled neural networks (FACNNs) is investigated in this paper. Using the properties of gamma function and special matrix, some criteria for bipartite Mittag–Leffler (M–L) synchronization and bipartite finite time synchronization of FACNNs have been obtained. To achieve bipartite finite time pinning synchronization, hybrid control strategy is designed. That is, finite time control combined with pinning control, pinning partial nodes, which can access the information of the leader. The upper bound of synchronization setting time is obtained.

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

Similar content being viewed by others

References

  1. Pldlubny I (1999) Fractional differential equations. Academic Press, New York

    Google Scholar 

  2. Oldham KB (2010) Fractional differential equations in electrochemistry. Adv Eng Softw 41(1):9–12

    Article  Google Scholar 

  3. Chen L, Wu R, He Y et al (2015) Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties. Appl Math Comput 257:274–284

    MathSciNet  MATH  Google Scholar 

  4. Chen L, Cao J, Wu R et al (2017) Stability and synchronization of fractional-order memristive neural networks with multiple delays. Neural Netw 94:76–85

    Article  Google Scholar 

  5. Lundstrom BN, Higgs MH, Spain WJ et al (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11(11):1335–1342

    Article  Google Scholar 

  6. Yu W, Li Y, Wen G et al (2016) Observer design for tracking consensus in second-order multi-agent systems: fractional order less than two. IEEE Trans Autom Control 62(2):894–900

    Article  MathSciNet  Google Scholar 

  7. Zhang L, Yang Y (2019) Stability analysis of fractional order Hopfield neural networks with optimal discontinuous control. Neural Process Lett 50(1):581–593

    Article  Google Scholar 

  8. Li H, Hu C, Cao J et al (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw pp 102–109

  9. Li H, Cao J, Hu C et al (2019) Global synchronization between two fractional-order complex networks with non-delayed and delayed coupling via hybrid impulsive control. Neurocomputing, pp 31–39

  10. Chen L, Huang T, Machado JA et al (2019) Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Neural Netw 118:289–299

    Article  Google Scholar 

  11. Chen L, Yin H, Huang T et al (2020) Chaos in fractional-order discrete neural networks with application to image encryption. Neural Netw 125:174–184

    Article  Google Scholar 

  12. Zhang L, Yang Y (2019) Optimal quasi-synchronization of fractional-order memristive neural networks with PSOA. Neural Comput Appl pp 1–16

  13. Huang C, Li H, Cao J (2019) A novel strategy of bifurcation control for a delayed fractional predator-prey model. Appl Math Comput 347:808–838

    Article  MathSciNet  Google Scholar 

  14. Bao H, Park JH, Cao J (2019) Neural Networks, Non-fragile state estimation for fractional-order delayed memristive BAM neural networks, pp 190–199

  15. Yu W, Cao J, Lü J (2008) Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM J Appl Dyn Syst 7(1):108–133

    Article  MathSciNet  Google Scholar 

  16. Li Y, Lou J, Wang Z et al (2018) Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Franklin Insti Eng Appl Math 355(14):6520–6530

    Article  MathSciNet  Google Scholar 

  17. Altafini C (2012) Consensus problems on networks with antagonistic interactions. IEEE Trans Autom Control 58(4):935–946

    Article  MathSciNet  Google Scholar 

  18. Wen G, Wang H, Yu X et al (2017) Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Trans Circuits Syst II Express Briefs 65(9):1204–1208

    Article  Google Scholar 

  19. Liu F, Song Q, Wen G et al (2018) Bipartite synchronization in coupled delayed neural networks under pinning control. Neural Netw 108:146–154

    Article  Google Scholar 

  20. Lu J, Wang Y, Shi X (2019) Finite-time bipartite consensus for multiagent systems under detail-balanced antagonistic interactions, IEEE Trans Syst Man Cybernet 1–9

  21. Song Q, Lu G, Wen G et al (2019) Bipartite synchronization and convergence analysis for network of harmonic oscillator systems with signed graph and time delay. IEEE Trans Circuits Syst I Regul Pap 66(7):2723–2734

    Article  MathSciNet  Google Scholar 

  22. Song Q, Cao J, Liu F (2012) Pinning synchronization of linearly coupled delayed neural networks. Math Comput Simul 86:39–51

    Article  MathSciNet  Google Scholar 

  23. Huang C, Zhang X, Lam HK et al (2020) Synchronization analysis for nonlinear complex networks with reaction-diffusion terms using fuzzy model based approach. IEEE Trans Fuzzy Syst pp 1–1

  24. Yang X, Li X, Lu J, et al (2019) Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control. IEEE Trans Syst Man Cybernet, pp 1-10

  25. Huang C, Lu J, Ho DW et al (2020) Stabilization of probabilistic boolean networks via pinning control strategy. Inf Sci pp 205–217

  26. Li H, 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

    Article  MathSciNet  Google Scholar 

  27. Wang F, Yang Y (2018) Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes. Appl Math Comput 339:1–14

    Article  MathSciNet  Google Scholar 

  28. Zhang L, Yang Y (2020) Finite time impulsive synchronization of fractional order memristive BAM neural networks. Neurocomputing 384:213–224

    Article  Google Scholar 

  29. Xiao J, Zhong S, Li Y 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 

  30. Velmurugan G, Rakkiyappan R, Cao J (2016) Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Netw 73:36–46

    Article  Google Scholar 

  31. Zheng M, Li L, Peng H et al (2017) Finite-time projective synchronization of memristor-based delay fractional-order neural networks. Nonlinear Dyn 89(4):2641–2655

    Article  MathSciNet  Google Scholar 

  32. Li HL, Cao J, Jiang H et al (2018) Finite-time synchronization of fractional-order complex networks via hybrid feedback control. Neurocomputing 320:69–75

    Article  Google Scholar 

  33. Kilbas AAA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, New York

    MATH  Google Scholar 

  34. Monje CA, Chen YQ, Vinagre BM et al (2010) Fractional-order systems and controls: fundamentals and applications. Springer Science & Business Media, Berlin

    Book  Google Scholar 

  35. Aguila-Camacho N, Duarte-Mermoud MA, Gallegos JA (2014) Lyapunov functions for fractional order systems. Commun Nonlinear Sci Numer Simul 19(9):2951–2957

    Article  MathSciNet  Google Scholar 

  36. Wu H, Wang L, Niu P, Wang Y (2017) Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy. Neurocomputing 235:264–273

    Article  Google Scholar 

  37. Chen T, Liu X, Lu W (2007) Pinning complex networks by a single controller. IEEE Trans Circuits Syst I Regul Pap 54(6):1317–1326

    Article  MathSciNet  Google Scholar 

  38. Horn RA, Johnson CR (2012) Matrix analysis. Cambridge University Press, Cambridge

    Book  Google Scholar 

  39. Hardy G, Littlewood J, Polya G (1988) Inequalities. Cambridge University Press, Cambridge

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering and Automation, Changshu Institute of Technology, Changshu, 215500, Jiangsu, PR China

    Lingzhong Zhang

  2. School of IoT Engineering, Jiangnan University, Wuxi, 214122, PR China

    Yongqing Yang

Authors
  1. Lingzhong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongqing Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongqing Yang.

Additional information

Publisher's Note

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

This work was supported by the National Natural Science Foundation of China Nos. 61803049 and 61901062.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Yang, Y. Bipartite Synchronization Analysis of Fractional Order Coupled Neural Networks with Hybrid Control. Neural Process Lett 52, 1969–1981 (2020). https://doi.org/10.1007/s11063-020-10332-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-020-10332-6

Keywords

Search

Navigation