[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Journal of Vibration Testing and System Dynamics 9(3) (2025) 281--290 | DOI:10.5890/JVTSD.2025.09.006

Vijay K. Shukla

Department of Mathematics, D.S.B. Campus, Kumaun University, Nainital-263001, Uttarakhand, India

Download Full Text PDF

 

Abstract

This study examines the synchronization between distributed-order chaotic systems. The primary goal is to construct control functions to synchronize the distributed-order drive and response systems by implementing Laplace transform. In addition, the fundamental characteristics of chaotic systems are examined. We describe a strategy for introducing generalized synchronization between distributed-order chaotic systems. We also discuss inverse generalized synchronization between chaotic systems with different dimensions. Ultimately, numerical simulations confirm the accuracy of the acquired outcomes.

References

  1. [1]  Pecora, L.M. and Carroll, T.L. (1990), Synchronization in chaotic systems, Physical Review Letters, 64(8), 821.
  2. [2]  Srivastava, M., Das, S., and Leung, A.Y.T. (2013), Hybrid phase synchronization between identical and non-identical three dimensional chaotic systems using active control method, Nonlinear Dynamics, 73, 2261-2272.
  3. [3]  Gonzalez-Miranda, J.M. (2002), Generalized synchronization in directionally coupled systems with identical individual dynamics, Physical Review E, 65, 047202.
  4. [4]  Ucar, A., Lonngren, K.E., and Bai, E.W. (2008), Multi-switching synchronization of chaotic systems with active controllers, Chaos, Solitons and Fractals, 38(1), 254-262.
  5. [5]  Gasri, A., Ouannas, A., Ojo, K.S., and Pham, V.T. (2018), Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems, Nonlinear Analysis: Modelling and Control, 23(4), 583-598.
  6. [6]  Yadav, V.K., Shukla, V.K., and Das, S. (2019), Difference synchronization among three chaotic systems with exponential term and its chaos control, Chaos, Solitons and Fractals, 124, 36-51.
  7. [7]  Hunt, B.R., Ott, E., and Yorke, J.A. (1997), Differentiable generalized synchronization of chaos, Physical Review E, 55(4), 4029-4034.
  8. [8]  Zhang, G., Liu, Z., and Ma, Z. (2007), Generalized synchronization of different dimensional chaotic dynamical systems, Chaos, Solitons and Fractals, 32, 773-779.
  9. [9]  Li, R.H. (2009), Exponential generalized synchronization of uncertain coupled chaotic systems by adaptive control, Communications in Nonlinear Science and Numerical Simulation, 14, 2757-2764.
  10. [10]  El-Sayed, A.M.A., Elsaid, A., Nour, H.M., and Elsonbaty, A. (2014), Synchronization of different dimensional chaotic systems with time varying parameters, disturbances and input nonlinearities, Journal of Applied Analysis and Computation, 4(4), 323-338.
  11. [11]  Gu, B., Shan, L., Li J., and Wang, Z. (2008), Generalized Projected Synchronization of Wang and Chen hyperchaotic Systems, Proceedings of the 7${^{th}$ World Congress on Intelligent Control and Automation}, 8626-8631.
  12. [12]  Wang, X., Wang, L., and Lin, D. (2012), Generalized (lag, anticipated and complete) projective synchronization in two non-identical chaotic systems with unknown parameters, International Journal of Modern Physics B, 26(16), 1-9.
  13. [13]  Shukla, V.K. (2024), Finite-time generalized and modified generalized projective synchronization between chaotic and hyperchaotic systems with external disturbances, Discontinuity, Nonlinearity, and Complexity, 13(1), 157-172.
  14. [14]  Ouannas, A. (2015), A new generalized-type of synchronization for discrete-time chaotic dynamical systems, Journal of Computational and Nonlinear Dynamics, 10(6), 061019.
  15. [15]  Ouannas, A., Azar, A.T., and Ziar, T. ( 2017), On inverse full state hybrid function projective synchronization for continuous-time chaotic dynamical systems with arbitrary dimensions, Differential Equations and Dynamical Systems, 28(4), 1045-1058.
  16. [16]  Ouannas, A., Azar, A.T., and Radwan, A.G. (2016), On inverse problem of generalized synchronization between different dimensional integer-order and fractional-order chaotic systems, 28th International Conference on Microelectronics (ICM), 193-196.
  17. [17]  Khennaoui, A.A., Ouannas, A., Bendoukha, S., Grassi, G., Wang, X., and Pham, V.T. (2018), Generalized and inverse generalized synchronization of fractional-order discrete-time chaotic systems with non-identical dimensions, Advances in Difference Equations, 303, 1-14.
  18. [18]  Lu, Z. and Bassett, D.S. (2020), Invertible generalized synchronization: A putative mechanism for implicit learning in neural systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(6), 1-20.
  19. [19]  Ding, W., Patnaik, S., Sidhardh, S., and Semperlotti, F. (2021), Applications of distributed-order fractional operators, Entropy, 23(1), 1-43.
  20. [20]  Fern{a}ndez-Anaya, G., Nava-Antonio, G., Jamous-Galante, J., Mu\~{n}oz-Vega, R., and Hern{a}ndez-Mart{i}nez, E.G. (2017), Asymptotic stability of distributed order nonlinear dynamical systems, Communications in Nonlinear Science and Numerical Simulation, 48, 541-549.
  21. [21]  Caputo, M. (1969), Elasticita e dissipazione, Zanichelli.
  22. [22]  Lorenzo, C.F. and Hartley, T.T. (2002), Variable order and distributed order fractional operators, Nonlinear Dynamics, 29, 57-98.
  23. [23]  Oustaloup, A. (2014), \text{Diversity and Non-Integer Differentiation for System Dynamics}, John Wiley \& Sons.
  24. [24]  Lorenzo, C.F. and Hartley, T.T. (1998), Initialization, conceptualization, and application in the generalized fractional calculus, NASA, 208415.
  25. [25]  Hartley, T.T. and Lorenzo, C.F. (1999), Fractional system identification: An approach using continuous order distributions, NASA, 209640.
  26. [26]  Aminikhah, H., Refahi Sheikhani, A., and Rezazadeh, H. (2013), Stability analysis of distributed-order fractional Chen system, The Scientific World Journal, 1-13.
  27. [27]  Podlubny, I. (1998), Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier.
  28. [28]  Mahmoud, G.M., Farghaly, A.A., Abed-Elhameed, T.M., Aly, S.A., and Arafa, A.A. (2020), Dynamics of distributed-order hyperchaotic complex van der Pol oscillators and their synchronization and control, The European Physical Journal Plus, 135(1), 1-16.
  29. [29]  Duffy, D.G. (2004), Transform Methods for Solving Partial Differential Equations, CRC Press.
  30. [30]  Baleanu, D., Zibaei, S., Namjoo, M., and Jajarmi, A. (2021), A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system, Advances in Difference Equations, 308, 1-19.
  31. [31]  Xin, L., Shi, X., and Xu, M. (2022), Dynamical analysis and generalized synchronization of a novel fractional-order hyperchaotic system with hidden attractor, Axioms, 12(1), 1-12.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates