Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

: pp. 486–498
Received: May 22, 2021
Revised: July 06, 2021
Accepted: July 08, 2021
Government Arts College, Coimbatore, India
Government Arts College, Coimbatore, India; Sri Ramakrishna College of Arts and Science, Coimbatore, India

This paper deals with the problem of finite-time projective synchronization for a class of neutral-type complex-valued neural networks (CVNNs) with time-varying delays.  A simple state feedback control protocol is developed such that slave CVNNs  can be projective synchronized with the master system in finite time.  By employing inequalities technique and designing new Lyapunov--Krasovskii functionals, various novel and easily verifiable conditions are obtained to ensure the finite-time projective synchronization.  It is found that the settling time can be explicitly calculated for the neutral-type CVNNs.  Finally, two numerical simulation results are demonstrated to validate the theoretical results of this paper.

  1. Zhu Z., Lu J.-G.  Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach.  Applied Mathematics and Computation. 401, 126075 (2021).
  2. Wang Y., Li D.  Adaptive synchronization of chaotic systems with time-varying delay via aperiodically intermittent control.  Soft Computing. 24, 12773–12780 (2020).
  3. Liu D., Li H., Wang D.  Online synchronous approximate optimal learning algorithm for multi-player non-zero-sum games with unknown dynamics.  IEEE Transactions on Systems, Man, and Cybernetics: Systems. 44 (8), 1015–1027 (2014).
  4. Cao Y., Cao Y., Guo Z., Huang T., Wen\  S.  Global exponential synchronization of delayed memristive neural networks with reaction–diffusion terms.  Neural Networks. 123, 70–81 (2020).
  5. Selvaraj P., Sakthivel R., Kwon O. M.  Synchronization of fractional-order complex dynamical network with random coupling delay, actuator faults and saturation.  Nonlinear Dynamics. 94, 3101–3116 (2018).
  6. Wang C., Rathinasamy S.  Double almost periodicity for high-order hopfield neural networks with slight vibration in time variables.  Neurocomputing. 282, 1–15 (2018).
  7. Zhu J., Sun J.  Stability of quaternion-valued neural networks with mixed delays.  Neural Processing Letters. 49, 819–833 (2019).
  8. Jayanthi N., Santhakumari R.  Synchronization of time invariant uncertain delayed neural networks in finite time via improved sliding mode control.  Mathematical Modeling and Computing. 8 (2), 228–240 (2021).
  9. Arik S.  A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays.  Journal of the Franklin Institute. 356 (1), 276–291 (2019).
  10. Yogambigai J., Ali M. S., Alsulami H., Alhodaly M. S.  Global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays.  Chinese Journal of Physics. 65, 513–525 (2020).
  11. Faydasicok O.  New criteria for global stability of neutral-type Cohen-Grossberg neural networks with multiple delays.  Neural Networks. 125, 330–337 (2020).
  12. Jian J.,  Duan L.  Finite-time synchronization for fuzzy neutral-type inertial neural networks with time-varying coefficients and proportional delays.  Fuzzy Sets and Systems. 381, 51–67 (2020).
  13. Lien C. H., Yu K. W., Lin Y. F., Chung V. J.,  Chung L. Y.  Stability criteria of quaternion-valued neutral-type delayed neural networks.  Neurocomputing. 412, 287–294 (2020).
  14. Tu Z., Wang L.  Global Lagrange stability for neutral type neural networks with mixed time-varying delays.  International Journal of Machine Learning and Cybernetics. 9, 599–609 (2018).
  15. Ahmad I., Shafiq M.  Oscillation free robust adaptive synchronization of chaotic systems with parametric uncertainties.  Transactions of the Institute of Measurement and Control. 42 (11), 1977–1996 (2020).
  16. Bao H., Cao J.  Finite-time generalized synchronization of nonidentical delayed chaotic systems.  Nonlinear Analysis: Modelling and Control. 21 (3), 306–324 (2016).
  17. Yang S., Yu J., Hu C., Jiang H.  Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks.  Neural Networks. 104, 104–113 (2018).
  18. Zheng M., Li L., Peng H., Xiao J., Yang Y.,  Zhao H.  Finite-time projective synchronization of memristor-based delay fractional-order neural networks.  Nonlinear Dynamics. 89, 2641–2655 (2017).
  19. Wen S., Bao G., Zeng Z., Chen Y., Huang T.  Global exponential synchronizatin of memristor-based recurrent neural networks with time-varying delays.  Neural Networks. 48, 195–203 (2013).
  20. Wang Y.,  Cao J.  Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems.  Nonlinear Analysis: Real World Applications. 14 (1), 842–851 (2013).
  21. Skardal P. S., Sevilla-Escoboza R., Vera-{\'A}vila V. P., Buld{\'u} J. M.  Optimal phase synchronization in networks of phase-coherent chaotic oscillators.  Chaos: An Interdisciplinary Journal of Nonlinear Science. 27, 013111 (2017).
  22. Wang X., He Y.  Projective synchronization of fractional order chaotic system based on linear separation.  Physics Letters A. 372 (4), 435–441 (2008).
  23. Su B., Chunyu D.  Finite-time optimization stabilization for a class of constrained switched nonlinear systems.  Mathematical Problems in Engineering. 2018, Article ID: 6824803 (2018).
  24. Wei R., Cao J., Alsaedi A.  Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays.  Cognitive neurodynamics. 12, 121–134 (2018).
  25. Li L., Tu Z., Mei J.,  Jian J.  Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods.  Nonlinear Dynamics. 85, 375–388 (2016).
  26. Liu X., Su H., Chen M. Z. Q.  A switching approach to designing finite-time synchronizing controllers of couple neural networks.  IEEE Transactions on Neural Networks and Learning Systems. 27, 471–482 (2015).
  27. Chengrong X., Yu X., Qing X., Tong D., Xu Y.  Finite-time synchronization of complex dynamical networks with nondelayed and delayed coupling by continuous function controller.  Discrete Dynamics in Nature and Society. 2020, Article ID: 4171585 (2020).
  28. Xu Y., Shen R.,  Li W.  Finite-time synchronization for coupled systems with time delay and stochastic disturbance under feedback control.  Journal of Applied Analysis & Computation. 10 (1), 1–24 (2020).
  29. Claire W., Filippo D. B., Erica W., Ethan K. S., Dirk T., Herwig B., Ehud Y. I.  Optogenetic dissection of a behavioural module in the vertebrate spinal cord.  Nature. 461, 407–410 (2009).
  30. Ijspeert A. J.  Central pattern generators for locomotion control in animals and robots: a review.  Neural Networks. 21 (4), 642–653 (2008).
  31. Kaneko K.  Relevance of dynamic clustering to biological networks.  Physica D: Nonlinear Phenomena. 75 (1–3), 55–73 (1994).
  32. Rulkov N. F.  Images of synchronized chaos: Experiments with circuits.  Chaos. 6, 262–279 (1996).
  33. Hindmarsh J. L., Rose R. M.  A model of the nerve impulse using two first-order differential equations.  Nature. 296, 162–164 (1982).
  34. Hindmarsh J. L., Rose R. M.  A model of neuronal bursting using three coupled first order differential equations.  Proceedings of the Royal society of London, Series B, Biological sciences. 221, 87–102 (1984).
Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 486–498 (2021)