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Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method

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Abstract

This article is concerned with the fixed time synchronization for a class of Quaternion valued neural networks (QVNNs) with mixed time varying delays. Firstly, the QVNNs are separated into four equivalent real valued neural networks (RVNNs). Then, a novel suitable controller is designed to establish the fixed time synchronization of the QVNNs with the help of Lyapunov function. To give a glimpse, the finite time and fixed time stability definitions are proposed. Two different expressions of settling time are obtained by using two different lemmas. Finally, the validation of the theoretical results is shown through numerical simulation to a specific example.

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References

  1. Shen D, Xu Y (2016) Iterative learning control for discrete-time stochastic systems with quantized information. IEEE/CAA J Autom Sin 3(1):59–67

    Article  MathSciNet  Google Scholar 

  2. Zhao D, Wang Z, Chen Y, Wei G (2020) Proportional-integral observer design for multidelayed sensor-saturated recurrent neural networks: a dynamic event-triggered protocol. IEEE Trans Cybern 50(11):4619–4632

    Article  Google Scholar 

  3. Liu Y, Zheng Y, Lu J, Cao J, Rutkowski L (2019) Constrained quaternion-variable convex optimization: a quaternion-valued recurrent neural network approach. IEEE Trans Neural Netw Learn Syst 31(3):1022–1035

    Article  MathSciNet  Google Scholar 

  4. Miao J, Kou KI (2020) Quaternion-based bilinear factor matrix norm minimization for color image inpainting. IEEE Trans Signal Process 68:5617–5631

    Article  MathSciNet  Google Scholar 

  5. Xia Z, Liu Y, Lu J, Cao J, Rutkowski L (2020) Penalty method for constrained distributed quaternion-variable optimization. IEEE Trans Cybern

  6. Zhao Z, Wang Z, Zou L, Guo G (2018) Finite-time state estimation for delayed neural networks with redundant delayed channels. IEEE Trans Syst Man Cybern Syst

  7. Ding D, Wang Z, Han QL (2019) Neural-network-based output-feedback control with stochastic communication protocols. Automatica 106:221–229

    Article  MathSciNet  MATH  Google Scholar 

  8. Jin J (2021) An improved finite time convergence recurrent neural network with application to time-varying linear complex matrix equation solution. Neural Process Lett 53(1):777–786

    Article  Google Scholar 

  9. Wang Z, Liu X (2019) Exponential stability of impulsive complex-valued neural networks with time delay. Math Comput Simul 156:143–157

    Article  MathSciNet  MATH  Google Scholar 

  10. Rakkiyappan R, Sivaranjani R, Velmurugan G, Cao J (2016) Analysis of global O (t- \(\alpha \)) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays. Neural Netw 77:51–69

    Article  MATH  Google Scholar 

  11. Wang JL, Wu HN, Huang T, Ren SY (2014) Passivity and synchronization of linearly coupled reaction–diffusion neural networks with adaptive coupling. IEEE Trans Cybern 45(9):1942–1952

    Article  Google Scholar 

  12. Wen S, Zeng Z, Huang T, Zhang Y (2013) Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans Fuzzy Syst 22(6):1704–1713

    Article  Google Scholar 

  13. Zeng D, Zhang R, Park JH, Zhong S, Cheng J, Wu GC (2021) Reliable stability and stabilizability for complex-valued memristive neural networks with actuator failures and aperiodic event-triggered sampled-data control. Nonlinear Anal Hybrid Syst 39:100977

    Article  MathSciNet  MATH  Google Scholar 

  14. Took CC, Mandic DP (2008) The quaternion LMS algorithm for adaptive filtering of hypercomplex processes. IEEE Trans Signal Process 57(4):1316–1327

    Article  MathSciNet  MATH  Google Scholar 

  15. Miron S, Le Bihan N, Mars JI (2006) Quaternion-MUSIC for vector-sensor array processing. IEEE Trans Signal Process 54(4):1218–1229

    Article  MATH  Google Scholar 

  16. Xia Y, Jahanchahi C, Mandic DP (2014) Quaternion-valued echo state networks. IEEE Trans Neural Netw Learn Syst 26(4):663–673

    MathSciNet  Google Scholar 

  17. Zou C, Kou KI, 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 

  18. Isokawa T, Kusakabe T, Matsui N, Peper F (2003) Quaternion neural network and its application. In: International conference on knowledge-based and intelligent information and engineering systems, pp 318–324

  19. Qin S, Feng J, Song J, Wen X, Xu C (2016) 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 

  20. Sahoo A, Xu H, Jagannathan S (2015) Neural network-based event-triggered state feedback control of nonlinear continuous-time systems. IEEE Trans Neural Netw Learn Syst 27(3):497–509

    Article  MathSciNet  Google Scholar 

  21. Jiang BX, Liu Y, Kou KI, Wang Z (2020) Controllability and observability of linear quaternion-valued systems. Acta Math Sin Engl Ser 36(11):1299–1314

    Article  MathSciNet  MATH  Google Scholar 

  22. Duan L, Fang X, Fu Y (2019) Global exponential synchronization of delayed fuzzy cellular neural networks with discontinuous activations. Int J Mach Learn Cybern 10(3):579–589

    Article  Google Scholar 

  23. Yau HT, Hung TH, Hsieh CC (2012) Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption. Sensors 12(6):7468–7484

    Article  Google Scholar 

  24. Diab A, Marque C, Karlsson B, Hassan M (2013) Comparison of methods for evaluating signal synchronization and direction: application to uterine EMG signals. In: 2013 2nd international conference on advances in biomedical engineering, pp 14–17

  25. Cagnan H, Duff EP, Brown P (2015) The relative phases of basal ganglia activities dynamically shape effective connectivity in Parkinson’s disease. Brain 138(6):1667–1678

  26. Zhang H, Wang XY (2017) Complex projective synchronization of complex-valued neural network with structure identification. J Franklin Inst 354(12):5011–5025

    Article  MathSciNet  MATH  Google Scholar 

  27. Sun Y, Liu Y (2021) Adaptive synchronization control and parameters identification for chaotic fractional neural networks with time-varying delays. Neural Process Lett 1–17

  28. Li J, He C, Zhang W, Chen M (2017) Adaptive synchronization of delayed reaction–diffusion neural networks with unknown non-identical time-varying coupling strengths. Neurocomputing 219:144–153

    Article  Google Scholar 

  29. Kumar R, Kumar U, Das S, Qiu J, Lu J (2021) Effects of heterogeneous impulses on synchronization of complex-valued neural networks with mixed time-varying delays. Inf Sci 551:228–244

    Article  MathSciNet  Google Scholar 

  30. Li Y, Yang Z, Dong Z (2017) Asymptotical synchronization of memristor-based neural networks with time-varying delays via adaptive control. In: 2017 36th Chinese control conference (CCC), pp 4012–4017

  31. Mishra AK, Das S, Yadav VK (2021) Finite-time synchronization of multi-scroll chaotic systems with sigmoid non-linearity and uncertain terms. Chin J Phys

  32. Chen C, Li L, Peng H, Yang Y, Li T (2017) Finite-time synchronization of memristor-based neural networks with mixed delays. Neurocomputing 235:83–89

    Article  Google Scholar 

  33. Cai Z, Huang L, Zhu M, Wang D (2016) Finite-time stabilization control of memristor-based neural networks. Nonlinear Anal Hybrid Syst 20:37–54

    Article  MathSciNet  MATH  Google Scholar 

  34. Liu M, Jiang H, Hu C (2016) Finite-time synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. Neurocomputing 194:1–9

    Article  Google Scholar 

  35. 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  MATH  Google Scholar 

  36. Wu H, Wang X, Liu X, Cao J (2020) Finite/fixed-time bipartite synchronization of coupled delayed neural networks under a unified discontinuous controller. Neural Process Lett 52(2):1359–1376

    Article  Google Scholar 

  37. Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110

    Article  MathSciNet  MATH  Google Scholar 

  38. Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89:74–83

    Article  MATH  Google Scholar 

  39. Ni J, Liu L, Liu C, Hu X, Li S (2016) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155

    Google Scholar 

  40. Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen–Grossberg neural networks. Neural Netw 73:86–94

    Article  MATH  Google Scholar 

  41. Zhang Y, Deng S (2020) Fixed-time synchronization of complex-valued memristor-based neural networks with impulsive effects. Neural Process Lett 52(2):1263–1290

    Article  Google Scholar 

  42. Gao F, Wu Y, Zhang Z, Liu Y (2019) Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application. Nonlinear Anal Hybrid Syst 31:56–68

    Article  MathSciNet  MATH  Google Scholar 

  43. Jiang B, Hu Q, Friswell MI (2016) Fixed-time attitude control for rigid spacecraft with actuator saturation and faults. IEEE Trans Control Syst Technol 24(5):1892–1898

    Article  Google Scholar 

  44. Yang X, Li C, Song Q, Chen J, Huang J (2018) Global Mittag–Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 105:88–103

    Article  MATH  Google Scholar 

  45. Chen D, Zhang W, Cao J, Huang C (2020) Fixed time synchronization of delayed quaternion-valued memristor-based neural networks. Adv Differ Equ 1:1–16

    MathSciNet  MATH  Google Scholar 

  46. Kumar U, Das S, Huang C, Cao J (2020) Fixed-time synchronization of quaternion-valued neural networks with time-varying delay. Proc R Soc A 476(2241):20200324

    Article  MathSciNet  MATH  Google Scholar 

  47. 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 

  48. Ding D, You Z, Hu Y, Yang Z, Ding L (2020) Finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks. Int J Mod Phys B 2150032

  49. Deng H, Bao H (2019) Fixed-time synchronization of quaternion-valued neural networks. Phys A Stati Mech Appl 527(121351)

  50. Li T, Luo Q, Sun C, Zhang B (2009) Exponential stability of recurrent neural networks with time-varying discrete and distributed delays. Nonlinear Anal Real World Appl 10(4):2581–2589

    Article  MathSciNet  MATH  Google Scholar 

  51. Lakshmanan M, Senthilkumar DV (2011) Dynamics of nonlinear time-delay systems. Springer, Berlin

    Book  MATH  Google Scholar 

  52. Fiagbedzi YA, Pearson AE (1987) A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica 23(3):311–326

    Article  MathSciNet  MATH  Google Scholar 

  53. Hale JK, Lunel SMV (2013) Introduction to functional differential equations. Springer, Berlin, p 99

    Google Scholar 

  54. Cao J, Wang J (2004) Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw 17(3):379–390

    Article  MATH  Google Scholar 

  55. Chen C, Li L, Peng H, Yang Y, Mi L, Zhao H (2020) A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks. Neural Netw 123:412–419

    Article  MATH  Google Scholar 

  56. 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 

  57. Chen X, Zhao Z, Song Q, Hu J (2017) Multistability of complex-valued neural networks with time-varying delays. Appl Math Comput 294:18–35

    MathSciNet  MATH  Google Scholar 

  58. Li D, Ge SS, Lee TH (2020) Fixed-time-synchronized consensus control of multiagent systems. IEEE Trans Control Netw Syst 8(1):89–98

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The third author acknowledges the project Grant provided by the SERB, Government of India under the MATRICS scheme (File No.: MTR/2020/000053). The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia has funded this project, under grant no. (FP-114-43).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005, India

    Sunny Singh, Umesh Kumar & Subir Das

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

    F. Alsaadi

  3. School of Mathematics, Southeast University, Nanjing, 211189, People’s Republic of China

    Jinde Cao

  4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

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  1. Sunny Singh
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  2. Umesh Kumar
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  3. Subir Das
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  4. F. Alsaadi
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  5. Jinde Cao
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Correspondence to Jinde Cao.

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Singh, S., Kumar, U., Das, S. et al. Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method. Neural Process Lett 54, 785–801 (2022). https://doi.org/10.1007/s11063-021-10657-w

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