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Bipartite finite time synchronization for general Caputo fractional-order impulsive coupled networks

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Abstract

This briefly investigates the bipartite finite time synchronization in fractional-order impulsive signed networks (FISNs), where there exist antagonistic communication links between neighboring nodes. Firstly, some new judgment conditions about finite time stability of FISNs are given on generalized Caputo fractional-order derivative. Secondly, by using Dirac function and the grapy theory, FISNs are transformed to fractional-order impulsive differential equations, which shows that the impulsive effect on signed networks is dependent on the order of the addressed networks and impulsive function. Thirdly, to provide novel criteria for bipartite finite time synchronization of FISNs by using a low-dimensional linear matrix inequality, pinning impulsive control strategy is designed. Fourthly, an upper bound on setting time for synchronization is obtained, and the influence of order on setting time is analyzed. Finally, numerical simulation is provided for illustration.

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References

  1. Ma J, Zhang G, Hayat T, Ren G (2019) Model electrical activity of neuron under electric field. Nonlinear Dyn 95(2):1585–1598

    Google Scholar 

  2. Zhang Z, Cao J (2018) Novel finite-time synchronization criteria for inertial neural networks with time delays via integral inequality method. IEEE Trans Neural Netw Learn Syst 30(5):1476–1485

    MathSciNet  Google Scholar 

  3. Jia Q, Tang WKS (2018) Consensus of multi-agents with event-based nonlinear coupling over time-varying digraphs. IEEE Trans Circuits Syst II Express Briefs 65(12):1969–1973

    Google Scholar 

  4. Lakshmanan S, Prakash M, Lim CP, Rakkiyappan R, Balasubramaniam P, Nahavandi S (2016) Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Trans Neural Netw Learn Syst 29(1):195–207

    MathSciNet  Google Scholar 

  5. Song Q, Lu G, Wen G (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

    MathSciNet  Google Scholar 

  6. Liu F, Song Q, Wen G, Cao J, Yang X (2018) Bipartite synchronization in coupled delayed neural networks under pinning control. Neural Netw 108:146–154

    MATH  Google Scholar 

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

    Google Scholar 

  8. Jia Q, Sun M, Tang WKS (2019) Consensus of multiagent systems with delayed node dynamics and time-varying coupling. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/tsmc.2019.2921594

    Article  Google Scholar 

  9. Song Q, Lu G, Wen G, Cao J, Liu F (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

    MathSciNet  Google Scholar 

  10. Zhai S, Li Q (2016) Pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and switching topologies. Syst Control Lett 94:127–132

    MathSciNet  MATH  Google Scholar 

  11. Huang C, Nie X, Zhao X, Song Q, Tu Z, Xiao M, Cao J (2019) Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 117:67–93

    MATH  Google Scholar 

  12. Zhang S, Yu Y, Yu J (2016) LMI conditions for global stability of fractional-order neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2423–2433

    MathSciNet  Google Scholar 

  13. Ding Z, Zeng Z, Zhang H, Wang L, Wang L (2019) New results on passivity of fractional-order uncertain neural networks. Neurocomputing 351:51–59

    Google Scholar 

  14. Kaslik E, Radulescu IR (2017) Dynamics of complex-valued fractional-order neural networks. Neural Netw 89:39–49

    MATH  Google Scholar 

  15. Zamani M, Karimi-Ghartemani M, Sadati N (2007) FOPID controller design for robust performance using particle swarm optimization. Fract Calcul Appl Anal 10(2):169–187

    MathSciNet  MATH  Google Scholar 

  16. 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

    MathSciNet  MATH  Google Scholar 

  17. Behinfaraz R, Ghaemi S, Khanmohammadi S (2019) Adaptive synchronization of new fractional-order chaotic systems with fractional adaption laws based on risk analysis. Math Methods Appl Sci 42(6):1772–1785

    MathSciNet  MATH  Google Scholar 

  18. Zhang L, Yang Y, Zhang L, Yang Y (2019) Optimal quasi-synchronization of fractional-order memristive neural networks with PSOA. Neural Computing Appl 32(13):1–16

    Google Scholar 

  19. Zhang W, Zhang H, Cao J, Alsaadi FE, Chen D (2019) Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays. Neural Netw 110:186–198

    MATH  Google Scholar 

  20. Zhang W, Cao J, Wu R, Alsaadi FE, Alsaedi A (2019) Lag projective synchronization of fractional-order delayed chaotic systems. J Franklin Inst 356(3):1522–1534

    MathSciNet  MATH  Google Scholar 

  21. He S, Sun K, Wang H, Mei X, Sun Y (2018) Generalized synchronization of fractional-order hyperchaotic systems and its DSP implementation. Nonlinear Dyn 92(1):85–96

    Google Scholar 

  22. Gong P, Lan W (2018) Adaptive robust tracking control for multiple unknown fractional-order nonlinear systems. IEEE Trans Cybern 49(4):1365–1376

    Google Scholar 

  23. Yu Z, Jiang H, Hu C, Yu J (2017) Necessary and sufficient conditions for consensus of fractional-order multiagent systems via sampled-data control. IEEE Trans Cybern 47(8):1892–1901

    Google Scholar 

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

    Google Scholar 

  25. Zhang Z, Chen M, Li A (2020) Further study on finite-time synchronization for delayed inertial neural networks via inequality skills. Neurocomputing 373:15–23

    Google Scholar 

  26. Shen J, Lam J (2014) Non-existence of finite-time stable equilibria in fractional-order nonlinear systems. Automatica 50(2):547–551

    MathSciNet  MATH  Google Scholar 

  27. Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhao H (2017) Finite-time projective synchronization of memristor-based delay fractional-order neural networks. Nonlinear Dyn 89(4):2641–2655

    MathSciNet  MATH  Google Scholar 

  28. 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

    MATH  Google Scholar 

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

    Google Scholar 

  30. 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

    MathSciNet  MATH  Google Scholar 

  31. Pldlubny I (1999) Fractional differential equations. Academic press, New York

    Google Scholar 

  32. Kilbas AAA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier Science Limited, Amsterdam, p 204

    MATH  Google Scholar 

  33. Cao J, Chen G, Li P (2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans Syst Man Cybern Part B Cybern. 38(2):488–498

    Google Scholar 

  34. Wang Z, Yang D, Ma T, Sun N (2014) Stability analysis for nonlinear fractional-order systems based on comparison principle. Nonlinear Dyn 75(1–2):387–402

    MathSciNet  MATH  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

    MathSciNet  MATH  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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  38. 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

    MathSciNet  MATH  Google Scholar 

  39. Khalil HK (2004) Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems. IEEE Trans Autom Control 49(12):2173–2184

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  41. Zhang L, Yang Y (2018) Different impulsive effects on synchronization of fractional-order memristive BAM neural networks. Nonlinear Dyn 93(2):233–250

    MathSciNet  MATH  Google Scholar 

  42. Yang X, Li C, Huang T, Song Q, Huang J (2018) Global mittag-leffler synchronization of fractional-order neural networks via impulsive control. Neural Process Lett 48(1):459–479

    Google Scholar 

  43. Yang S, Hu C, Yu J, Jiang H (2019) Exponential stability of fractional-order impulsive control systems with applications in synchronization. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2019.2906497

    Article  Google Scholar 

  44. Song Q, Liu F, Cao J, Yu W (2012) \( M \)-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics. IEEE Trans Cybern 43(6):1688–1697

    Google Scholar 

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

    MATH  Google Scholar 

  46. Xiao J, Zhong S, Li Y (2017) Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays. Neurocomputing 219:431–439

    Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Changshu Institute of Technology, Changshu, 215500, People’s Republic of China

    Lingzhong Zhang

  2. School of Science, Wuxi Engineering Research Center for Biocomputing, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Yongqing Yang

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  1. Lingzhong Zhang
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Correspondence to Lingzhong Zhang.

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This work was jointly supported by the Natural Science Foundation of Jiangsu Province No.BK20170436 and the National Natural Science Foundation of China No.61803049.

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Zhang, L., Yang, Y. Bipartite finite time synchronization for general Caputo fractional-order impulsive coupled networks. Neural Comput & Applic 33, 2459–2470 (2021). https://doi.org/10.1007/s00521-020-05135-8

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  • DOI: https://doi.org/10.1007/s00521-020-05135-8

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