Skip to main content
SpringerLink
Log in

Global Dissipativity of Quaternion-Valued Fuzzy Cellular Fractional-Order Neural Networks With Time Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This article deals with the global dissipativity of Quaternion-Valued Fuzzy Cellular Fractional-Order Neural Networks (QVFCFONNs). The model is solved by separating it into four real-valued parts, forming an equivalent real system according to Hamilton’s multiplication rules. Our approach is mainly based on the Lyapunov functionals, Linear Matrix Inequalities (LMIs) approach and Laplace transformation. New sufficient conditions are derived to ensure the global dissipativity for the considered network model. Furthermore, the global attractive set is obtained which is positive invariant one. A numerical example along with it simulation is given to demonstrate the accuracy and validity of our obtained theoretical results.

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

Similar content being viewed by others

References

  1. Abdeljawad T, Jarad F, Alzabut J (2017) Fractional proportional differences with memory. The European Phys J Special Topics 226(16):3333–3354

    Google Scholar 

  2. Ali MS, Narayanan G, Nahavandi S, Wang JL, Cao J (2021) Global dissipativity analysis and stability analysis for fractional-order quaternion-valued neural networks with time delays. IEEE Trans on Systems, Man, and Cybernetics: Systems

  3. Aouiti C, Dridi F (2020) New results on interval general Cohen-Grossberg BAM neural networks. J of Syst Science and Complexity 33(4):944–967

    MathSciNet  MATH  Google Scholar 

  4. Aouiti C, Dridi F (2019) Piecewise asymptotically almost automorphic solutions for impulsive non-autonomous high-order Hopfield neural networks with mixed delays. Neural Comput and Appl 31(9):5527–5545

    Google Scholar 

  5. Aouiti C, Gharbia IB (2020) Piecewise pseudo almost-periodic solutions of impulsive fuzzy cellular neural networks with mixed delays. Neural Processing Letters 51(2):1201–1225

    Google Scholar 

  6. Aouiti C, Gharbia IB, Cao J, Alsaedi A (2019) Dynamics of impulsive neutral-type BAM neural networks. J of The Franklin Institute 356(4):2294–2324

    MathSciNet  MATH  Google Scholar 

  7. Aouiti C, Sakthivel R, Touati F (2020) Global dissipativity of fuzzy bidirectional associative memory neural networks with proportional delays. Iranian J of Fuzzy Syst 18(2):65–80. https://doi.org/10.22111/IJFS.2020.5709

    Article  MathSciNet  MATH  Google Scholar 

  8. Aouiti C, Sakthivel R, Touati F (2020) Global dissipativity of fuzzy cellular neural networks with inertial term and proportional delays. Int J of Syst Science 51(8):1392–1405

    MathSciNet  MATH  Google Scholar 

  9. Aouiti C, Sakthivel R, Touati F (2020) Global dissipativity of high-order Hopfield bidirectional associative memory neural networks with mixed delays. Neural Comput and Appl 32(14):10183–10197

    Google Scholar 

  10. Aouiti C, Touati F (2020) Global dissipativity of Clifford-valued multidirectional associative memory neural networks with mixed delays. Comput and Applied Math 39(4):1–21. https://doi.org/10.1007/s40314-020-01367-5

    Article  MathSciNet  MATH  Google Scholar 

  11. Aouiti C, Touati F (2021) Stability and global dissipativity for neutral-type fuzzy genetic regulatory networks with mixed delays. Comput and Applied Math 40:213. https://doi.org/10.1007/s40314-021-01604-5

    Article  MathSciNet  MATH  Google Scholar 

  12. Burton TA, Zhang B (2012) Fractional equations and generalizations of Schaefer’s and Krasnoselskii’s fixed point theorems. Nonlinear Analysis: Theory, Methods & Appli 75(18):6485–6495

    MathSciNet  MATH  Google Scholar 

  13. Chanthorn P, Rajchakit G, Thipcha J, Emharuethai C, Sriraman R, Lim CP, Ramachandran R (2020) Robust stability of complex-valued stochastic neural networks with time-varying delays and parameter uncertainties. Math 8(5):742

    Google Scholar 

  14. Chen B, Chen J (2016) Global \(O(t-\alpha )\) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays. Neural Netw 73:47–57

    MATH  Google Scholar 

  15. Chen L, Chai Y, Wu R, Ma T, Zhai H (2013) Dynamic analysis of a class of fractional-order neural networks with delay. Neurocomputing 111:190–194

    Google Scholar 

  16. Chen X, Li L, Li Z (2018) Robust stability analysis of quaternion-valued neural networks via LMI approach. Adv in Difference Equations 2018(1):1–20. https://doi.org/10.1186/s13662-018-1585-z

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen Z (2019) Convergence of neutral type fuzzy cellular neural networks with D operator. Neural Process Letters 49(3):1189–1199

    Google Scholar 

  18. De Leo S, Ducati G (2012) Delay time in quaternionic quantum mechanics. J of math phys 53(2):022102. https://doi.org/10.1063/1.3684747

    Article  MathSciNet  MATH  Google Scholar 

  19. Deng H, Bao H (2019) Fixed-time synchronization of quaternion-valued neural networks. Physica A: Statistical Mech and its Appl 527:121351

    MathSciNet  MATH  Google Scholar 

  20. Ding Z, Shen Y (2016) Global dissipativity of fractional-order neural networks with time delays and discontinuous activations. Neurocomputing 196:159–166

    Google Scholar 

  21. Ding Z, Zhang H, Zeng Z, Yang L, Li S (2021) Global Dissipativity and Quasi-Mittag-Leffler Synchronization of Fractional-Order Discontinuous Complex-Valued Neural Networks. IEEE Trans on Neural Netw and Learning Syst. https://doi.org/10.1109/TNNLS.2021.3119647

    Article  Google Scholar 

  22. Dutta BK, Arora LK (2013) On the existence and uniqueness of solutions of a class of initial value problems of fractional order. Math Sciences 7(1):1–12. https://doi.org/10.1186/2251-7456-7-17

    Article  MathSciNet  Google Scholar 

  23. Fan Y, Huang X, Wang Z, Li Y (2018) Global dissipativity and quasi-synchronization of asynchronous updating fractional-order memristor-based neural networks via interval matrix method. J of the Franklin Institute 355(13):5998–6025

    MathSciNet  MATH  Google Scholar 

  24. Gibbon JD, Holm DD, Kerr RM, Roulstone I (2006) Quaternions and particle dynamics in the Euler fluid equations. Nonlinearity 19(8):1969. https://doi.org/10.1088/0951-7715/19/8/011

    Article  MathSciNet  MATH  Google Scholar 

  25. Gu Y, Wang H, Yu Y (2020) Synchronization for fractional-order discrete-time neural networks with time delays. Applied Math and Comput 372:124995

    MathSciNet  MATH  Google Scholar 

  26. Hanson AJ, Ma H (1995) Quaternion frame approach to streamline visualization. IEEE Trans on Visualization and Comput Graphics 1(2):164–174

    Google Scholar 

  27. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Inter J of Mach Learning and Cybernetics 8(4):1323–1331

    Google Scholar 

  28. Hong DT, Sau NH, Thuan MV (2021) New Criteria for Dissipativity Analysis of Fractional-Order Static Neural Networks. Circuits, Syst, and Signal Processing 41:1–23. https://doi.org/10.1007/s00034-021-01888-2

    Article  Google Scholar 

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

  30. Li H, Li C, Zhang W, Xu J (2018) Global dissipativity of inertial neural networks with proportional delay via new generalized halanay inequalities. Neural Process Letters 48(3):1543–1561

    Google Scholar 

  31. Li HL, Jiang H, Cao J (2020) Global synchronization of fractional-order quaternion-valued neural networks with leakage and discrete delays. Neurocomputing 385:211–219

    Google Scholar 

  32. Li N, Cao J (2018) Global dissipativity analysis of quaternion-valued memristor-based neural networks with proportional delay. Neurocomputing 321:103–113

    Google Scholar 

  33. Li R, Gao X, Cao J, Zhang K (2019) Dissipativity and exponential state estimation for quaternion-valued memristive neural networks. Neurocomputing 363:236–245

    Google Scholar 

  34. Li Y, Qin J, Li B (2019) Periodic solutions for quaternion-valued fuzzy cellular neural networks with time-varying delays. Adv in Difference Equations 2019(1):1–23

    MathSciNet  MATH  Google Scholar 

  35. Liu J, Jian J (2019) Global dissipativity of a class of quaternion-valued BAM neural networks with time delay. Neurocomputing 349:123–132

    Google Scholar 

  36. Lv X, Li X (2017) Delay-dependent dissipativity of neural networks with mixed non-differentiable interval delays. Neurocomputing 267:85–94

    Google Scholar 

  37. Li X, Shen J, Akca H, Rakkiyappan R (2015) LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter. Applied Math and Comput 250:798–804

    MathSciNet  MATH  Google Scholar 

  38. Manivannan R, Samidurai R, Cao J, Alsaedi A, Alsaadi FE (2019) Non-fragile extended dissipativity control design for generalized neural networks with interval time-delay signals. Asian J of Control 21(1):559–580

    MathSciNet  MATH  Google Scholar 

  39. Miron S, Le Bihan N, Mars JI (2006) Quaternion-MUSIC for vector-sensor array processing. IEEE trans on signal processing 54(4):1218–1229

    MATH  Google Scholar 

  40. Nagamani G, Ramasamy S, Balasubramaniam P (2016) Robust dissipativity and passivity analysis for discrete-time stochastic neural networks with time-varying delay. Complexity 21(3):47–58

    MathSciNet  MATH  Google Scholar 

  41. Pratap A, Raja R, Alzabut J, Cao J, Rajchakit G, Huang C (2020) Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. Math. Methods in the Applied Sciences 43(10):6223–6253

    MathSciNet  MATH  Google Scholar 

  42. Qinggui W (1983) Quaternion transformation and its application to the displacement analysis of spatial mechanisms [J]. Acta Mech Sinica 1:54–61

    MATH  Google Scholar 

  43. Rajchakit G, Sriraman R, Boonsatit N, Hammachukiattikul P, Lim CP, Agarwal P (2021) Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects. Adv in Difference Equations 2021(1):1–21. https://doi.org/10.1186/s13662-021-03367-z

    Article  MathSciNet  MATH  Google Scholar 

  44. Rajchakit G, Chanthorn P, Niezabitowski M, Raja R, Baleanu D, Pratap A (2020) Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks. Neurocomputing 417:290–301

    Google Scholar 

  45. Rajchakit G, Kaewmesri P, Chanthorn P, Sriraman R, Samidurai R, Lim CP (2020) Global stability analysis of fractional-order quaternion-valued bidirectional associative memory neural networks. Math 8(5):801

    Google Scholar 

  46. Rajchakit G, Kaewmesri P, Chanthorn P, Sriraman R, Samidurai R, Lim CP (2020) Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability. Math 8(5):815

    Google Scholar 

  47. Chanthorn P, Rajchakit G, Kaewmesri P, Sriraman R, Lim CP (2020) A delay-dividing approach to robust stability of uncertain stochastic complex-valued hopfield delayed neural networks. Symmetry 12(5):683

    Google Scholar 

  48. Rajchakit G, Sriraman R (2021) Robust passivity and stability analysis of uncertain complex-valued impulsive neural networks with time-varying delays. Neural Process Letters 53(1):581–606

    Google Scholar 

  49. Rajchakit G, Sriraman R, Kaewmesri P, Chanthorn P, Lim CP, Samidurai R (2020) An extended analysis on robust dissipativity of uncertain stochastic generalized neural networks with Markovian jumping parameters. Symmetry 12(6):1035

    Google Scholar 

  50. Rajivganthi C, Rihan FA, Lakshmanan S (2019) Dissipativity analysis of complex-valued BAM neural networks with time delay. Neural Comput and Appl 31(1):127–137

    Google Scholar 

  51. Rakkiyappan R, Velmurugan G, Li X, O’Regan D (2016) Global dissipativity of memristor-based complex-valued neural networks with time-varying delays. Neural Comput and Appl 27(3):629–649

    Google Scholar 

  52. Sabatier JATMJ, Agrawal OP, Machado JT (2007) Advances in fractional calculus, vol 4. Springer, Dordrecht (No. 9)

    MATH  Google Scholar 

  53. Selvaraj P, Sakthivel R, Marshal Anthoni S, Rathika M, Yong-Cheol M (2016) Dissipative sampled-data control of uncertain nonlinear systems with time-varying delays. Complexity 21(6):142–154

    MathSciNet  Google Scholar 

  54. Shen S, Li B, Li Y (2018) Anti-periodic dynamics of quaternion-valued fuzzy cellular neural networks with time-varying delays on time scales. Discrete Dyn in Nature and Soc 2018. https://doi.org/10.1155/2018/5290786

  55. Son DT, Trinh H (2016) On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE trans on neural netw and learning syst 29(1):225–231

    MathSciNet  Google Scholar 

  56. Song Q, Cao J (2008) Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. J of the Franklin Institute 345(1):39–59

    MathSciNet  MATH  Google Scholar 

  57. Sriraman R, Rajchakit G, Lim CP, Chanthorn P, Samidurai R (2020) Discrete-time stochastic quaternion-valued neural networks with time delays: an asymptotic stability analysis. Symmetry 12(6):936

    Google Scholar 

  58. Took CC, Strbac G, Aihara K, Mandic DP (2011) Quaternion-valued short-term joint forecasting of three-dimensional wind and atmospheric parameters. Renewable Energy 36(6):1754–1760

    Google Scholar 

  59. Tu Z, Cao J, Alsaedi A, Alsaadi F (2017) Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw 88:125–133

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  61. Tu Z, Wang L, Zha Z, Jian J (2013) Global dissipativity of a class of BAM neural networks with time-varying and unbound delays. Commun in Nonlinear Science and Numerical Simulation 18(9):2562–2570

    MathSciNet  MATH  Google Scholar 

  62. Udwadia FE, Schutte AD (2010) An alternative derivation of the quaternion equations of motion for rigid-body rotational dynamics. J of Appl Mech 77(4):044505. https://doi.org/10.1115/1.4000917

    Article  Google Scholar 

  63. Velmurugan G, Rakkiyappan R, Vembarasan V, Cao J, Alsaedi A (2017) Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay. Neural Netw 86:42–53

    MATH  Google Scholar 

  64. Wang D, Xiao A (2015) Dissipativity and contractivity for fractional-order systems. Nonlinear Dyn 80(1):287–294

    MathSciNet  MATH  Google Scholar 

  65. Wang H, Yu Y, Wen G, Zhang S, Yu J (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23

    Google Scholar 

  66. Wei H, Wu B, Tu Z (2020) Passivity and passification of quaternion-valued memristive neural networks. Math Methods in the Applied Sciences 43(4):2032–2044

    MathSciNet  MATH  Google Scholar 

  67. Yang D, Li X, Qiu J (2019) Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonlinear Analysis: Hybrid Syst 32:294–305

    MathSciNet  MATH  Google Scholar 

  68. Yuan K, Cao J, Deng J (2006) Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing 69(13–15):1619–1627

    Google Scholar 

  69. Yang T, Yang LB, Wu CW, Chua LO (1996, June) Fuzzy cellular neural networks: theory. In: 1996 Fourth IEEE International Workshop on Cellular Neural Networks and Their Applications Proceedings (CNNA-96), pp 181-186. IEEE

  70. Yang T, Yang LB, Wu CW, Chua LO (199 6, June) Fuzzy cellular neural networks: applications. In: 1996 Fourth IEEE International Workshop on Cellular Neural Networks and Their Applications Proceedings (CNNA-96), pp 225-230. IEEE

  71. Yang X, Li C, Song Q, Huang T, Chen X (2016) Mittag-Leffler stability analysis on variable-time impulsive fractional-order neural networks. Neurocomputing 207:276–286

    Google Scholar 

  72. Zhao Y, Li X, Cao J (2020) Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency. Applied Math and Comput 386:125467

    MathSciNet  MATH  Google Scholar 

  73. Zou C, Kou KI, Wang Y (2016) Quaternion collaborative and sparse representation with application to color face recognition. IEEE Trans on image process 25(7):3287–3302

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Sciences of Bizerta, Department of Mathematics, Mathématiques et applications UR13ES47, University of Carthage, BP W, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & Farid Touati

Authors
  1. Chaouki Aouiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farid Touati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chaouki Aouiti.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C., Touati, F. Global Dissipativity of Quaternion-Valued Fuzzy Cellular Fractional-Order Neural Networks With Time Delays. Neural Process Lett 55, 481–503 (2023). https://doi.org/10.1007/s11063-022-10893-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10893-8

Keywords

Mathematics Subject Classification

Search

Navigation