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Fixed/Prescribed-Time Bipartite Synchronization of Coupled Quaternion-Valued neural Networks with Competitive Interactions

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Abstract

In this work, based on the signed graph theory, the model of quaternion-valued neural networks (QVNNs) with cooperative-competitive interaction is established. Based on the quaternion-valued signum function and some properties, a direct analytical method without separation is proposed and quaternion-valued control schemes are developed to investigate fixed-time bipartite synchronization (FXTBS) and prescribed-time bipartite synchronization (PTBS) of QVNNs. Lastly, simulation is performed to manifest the correctness of the theorems.

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References

  1. Hamilton WR (1866) Elements of quaternions. Longmans Green and CO, London

    Google Scholar 

  2. Took CC, Mandic DP (2009) The quaternion LMS algorithm for adaptive filtering of hypercomplex processes. IEEE Trans Signal Process 57(4):1316–1327

    Article  MathSciNet  MATH  Google Scholar 

  3. Pei S, Cheng C (1997) A novel block truncation coding of color images using a quaternion-moment-preserving principle. IEEE Trans Commun 45(5):583–595

    Article  Google Scholar 

  4. Shuai J, Chen Z, Liu R, Wu B (1995) The Hamilton neural network model recognition of the color patterns. Chinese J Comput 5:372–379

    Google Scholar 

  5. Zou C, Kou K, Wang Y (2016) Quaternion collaborative and sparse representation with application to color face recognition. IEEE Trans Image Process 25(7):3287–3302

    Article  MathSciNet  MATH  Google Scholar 

  6. Qin S, Feng J, Song J, Wen X, Xu C (2018) A one-layer recurrent neural network for constrained complex-variable convex optimization. IEEE Trans Neural Netw Learn Syst 29(3):534–544

    Article  MathSciNet  Google Scholar 

  7. Xia Y, Jahanchahi C, Mandic D (2015) Quaternion-valued echo state networks. IEEE Trans Neural Netw Learn Syst 26(4):663–673

    Article  MathSciNet  Google Scholar 

  8. Tu Z, Cao J, Alsaedi A, Hayat T (2017) Global dissipativity analysis for delayed quaternion-valued neural networks. Neural Netw 89:97–104

    Article  MATH  Google Scholar 

  9. Song Q, Chen X (2018) Multistability analysis of quaternion-valued neural networks with time delays. IEEE Trans Neural Netw Learn Syst 29(11):5430–5440

    Article  MathSciNet  Google Scholar 

  10. Chen X, Song Q (2019) State estimation for quaternion-valued neural networks with multiple time delays. IEEE Trans Syst Man Cyber Syst 49(11):2278–2287

    Article  Google Scholar 

  11. Wei R, Cao J, Abdel-Aty M (2021) Fixed-time synchronization of second-order MNNs in quaternion field. IEEE Trans Syst Man Cyber Syst 51(6):3587–3598

    Article  Google Scholar 

  12. Liu Y, Zhang D, Lou J, Lu J, Cao J (2018) Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans Neural Netw Learn Syst 29:4201–4211

    Article  Google Scholar 

  13. Xia Z, Liu Y, Kou K, Wang J (2021) Clifford-valued distributed optimization based on recurrent neural networks. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3139865

    Article  Google Scholar 

  14. Liu Y, Zheng Y, Lu J, Cao J, Rutkowski L (2020) Constrained quaternion-variable convex optimization: a quaternion-valued recurrent neural network approach. IEEE Trans Neural Netw Learn Syst 31:1022–1035

    Article  MathSciNet  Google Scholar 

  15. Xia Z, Liu Y, Lu J, Cao J, Rutkowski L (2021) Penalty method for constrained distributed quaternion-variable optimization. IEEE Trans Cyber 51:5631–5636

    Article  Google Scholar 

  16. Qi X, Bao H, Cao J (2019) Exponential input-to-state stability of quaternion-valued neural networks with time delay. Appl Math Comput 358:382–393

    MathSciNet  MATH  Google Scholar 

  17. Altafini C (2013) Consensus problems on networks with antagonistic interactions. IEEE Trans Autom Control 58:943–946

    Article  MathSciNet  MATH  Google Scholar 

  18. Hu J, Wu Y, Li T, Ghosh BK (2019) Consensus control of general linear multiagent systems with antagonistic interactions and communication noises. IEEE Trans Autom Control 64:2122–2127

    Article  MathSciNet  MATH  Google Scholar 

  19. Li N, Zheng W (2021) Bipartite synchronization of multiple memristor-based neural networks with antagonistic interactions. IEEE Trans Cyber 32(9):1642–1653

    MathSciNet  Google Scholar 

  20. Zhu S, Bao H, Cao J (2022) Bipartite synchronization of coupled delayed neural networks with cooperative-competitive interaction via event-triggered control. Phys A 600:127586

    Article  MathSciNet  MATH  Google Scholar 

  21. 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

    Article  MATH  Google Scholar 

  22. Mao K, Liu X, Cao J, Hu Y (2022) Finite-time bipartite synchronization of coupled neural networks with uncertain parameters. Phys A 585:126431

    Article  MathSciNet  MATH  Google Scholar 

  23. Lin S, Liu X (2022) Robust passivity and control for directed and multiweighted coupled dynamical networks. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3167139

    Article  Google Scholar 

  24. Lin S, Liu X (2022) Synchronization for multiweighted and directly coupled reaction-diffusion neural networks with hybrid coupling via boundary control. Inform Sci 607:620–637

    Article  Google Scholar 

  25. Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38:751–766

    Article  MathSciNet  MATH  Google Scholar 

  26. Tang Z, Park JH, Shen H (2018) Finite-time cluster synchronization of Lur’e networks: a nonsmooth approach. IEEE Trans Syst Man Cyber Syst 48:1213–1224

    Article  Google Scholar 

  27. Li Z, Liu X (2020) Finite time anti-synchronization of quaternion-valued neural networks with asynchronous time-varying delays. Neural Process Lett 52:2253–2274

    Article  Google Scholar 

  28. Peng T, Zhang J, Tu Z, Lu J, Lou J (2022) Finite-time synchronization of quaternion-valued neural networks with delays: a switching control method without decomposition. Neural Netw 148:37–47

    Article  Google Scholar 

  29. Selvaraj P, Sakthivel R, Kwon OM (2018) Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation. Neural Netw 48:154–165

    Article  MATH  Google Scholar 

  30. Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57:2106–2110

    Article  MathSciNet  MATH  Google Scholar 

  31. Ding X, Cao J, Alsaedi A, Hayat T (2017) Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions. Neural Netw 90:42–55

    Article  MATH  Google Scholar 

  32. Wei R, Cao J (2019) Fixed-time synchronization of quaternion-valued memristive neural networks with time delays. Neural Netw 113:1–10

    Article  MATH  Google Scholar 

  33. Wei W, Yu J, Wang L, Hu C, Jiang H (2022) Fixed/Preassigned-time synchronization of quaternion-valued neural networks via pure power-law control. Neural Netw 146:341–349

    Article  MATH  Google Scholar 

  34. Feng L, Yu J, Hu C, Yang C, Jiang H (2021) Nonseparation method-based finite/fixed-time synchronization of fully complex-valued discontinuous neural networks. IEEE Trans Cyber 51:3212–3223

    Article  Google Scholar 

  35. Peng T, Qiu J, Lu J, Tu Z, Cao J (2021) Finite-time and fixed-time synchronization of quaternion-valued neural networks with/without mixed delays: An improved one-norm method. IEEE Trans Neural Netw Learn Syst 99:1–13

    Google Scholar 

  36. Shao S, Liu X, Cao J (2021) Prespecified-time synchronization of switched coupled neural networks via smooth controllers. Neural Netw 133:32–39

    Article  MATH  Google Scholar 

  37. Hu C, He H, Jiang H (2021) Fixed/preassigned-time synchronization of complex networks via improving fixed-time stability. IEEE Trans Cyber 51:2882–2892

    Article  Google Scholar 

  38. Liu X, Ho Daniel WC, Xie C (2020) Prespecified-time cluster synchronization of complex networks via a smooth control approach. IEEE Trans Cyber 50:1771–1775

    Article  Google Scholar 

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Funding

This research was supported by Natural Science Foundation of Jiangsu Province under Grant No. BK20210635.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Ruoyu Wei

  2. School of Mathematics, Frontiers Science Center for Mobile Information Communication and Security, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

    Fawaz E. Alsaadi

Authors
  1. Ruoyu Wei
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  2. Jinde Cao
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  3. Fawaz E. Alsaadi
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Correspondence to Ruoyu Wei.

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Wei, R., Cao, J. & Alsaadi, F.E. Fixed/Prescribed-Time Bipartite Synchronization of Coupled Quaternion-Valued neural Networks with Competitive Interactions. Neural Process Lett 55, 9765–9785 (2023). https://doi.org/10.1007/s11063-023-11225-0

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