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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Difference-Difference Synchronizations of Chaotic and Hyperchaotic Systems

Journal of Applied Nonlinear Dynamics 11(2) (2022) 487--497 | DOI:10.5890/JAND.2022.06.015

Eric Donald Dongmo$^{1,2, 3}$, Kayode Stephen Ojo$^{2}$, Paul Woafo$^{3 }$, Abdulahi Ndzi Njah$^{2}$

$^{1}$ Department of Mechanical Engineering, College of Technology, University of Buea, P. O. Box 63. Buea,

Cameroon

$^{2 }$ Department of Physics, University of Lagos, Akoka, Yaba, Lagos, Nigeria

$^3$ Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes and TWAS Research

, Cameroon

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Abstract

This paper investigates a new synchronization Difference-Difference Synchronization (DDS), based on drive response configuration via the active backstepping technique. In this new synchronization scheme, the difference between the state variables of two master systems synchronizes with the difference between the state variables of two response systems. The proposed DDS scheme is investigated using four chaotic systems and four hyperchaotic systems evolving from different initial conditions. The analytical and numerical simulations show the feasibility and the effectiveness of the proposed synchronization scheme.

Acknowledgments

Eric Donald Dongmo thanks the African-German Network of Excellence in Science (AGNES) for granting a Mobility Grant in 2016; the Grant is generously sponsored by German Federal Ministry of Education and Research and supported by the Alexander von Humboldt Foundation.

References

  1. [1]  Chen, G.R. and Dong, X. (1998), From Chaos to Order Methodologies, Perspectives and Applications World Scientific, Singapore (1998).
  2. [2]  Gross, N., Kinzel, W., Kanter, I., Rosenbluh, M., and Khaykovich, L. (2006), Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers, Optics communications, 267(2), 464-468.
  3. [3]  Blasius, B. and Stone, L. (2000), Chaos and phase synchronization in ecological systems. International Journal of Bifurcation and Chaos, 10(10), 2361-2380.
  4. [4]  Andrievskii, B.R. and Fradkov, A.L. (2004), Control of chaos: methods and applications. II. Applications. Automation and remote control, 65(4), 505-533.
  5. [5]  Feng, J., Jirsa, V.K., and Ding, M. (2006), Synchronization in networks with random interactions: theory and applications, Chaos: An Interdisciplinary Journal of Nonlinear Science, 16(1), 015109.
  6. [6]  Ma, M., Zhou, J., and Cai, J. (2012), Practical synchronization of nonautonomous systems with uncertain parameter mismatch via a single state feedback control, International Journal of Modern Physics C, 23(11), 1250073.
  7. [7]  Njah, A.N. and Ojo, K.S. (2010), Backstepping control and synchronization of parametrically and externally excited $\Phi $6 van der pol oscillators with application to secure communications. International Journal of Modern Physics B, 24(23), 4581-4593.
  8. [8]  Zribi, M., Smaoui, N., and Salim, H. (2009), Synchronization of the unified chaotic systems using a sliding mode controller, Chaos, Solitons {$\&$ Fractals}, 42(5), 3197-3209.
  9. [9]  Lu, J., Ho, D.W., Cao, J., and Kurths, J. (2013), Single impulsive controller for globally exponential synchronization of dynamical networks, Nonlinear Analysis: Real World Applications, 14(1), 581-593.
  10. [10]  Gholizade-Narm, H., Azemi, A., and Khademi, M. (2013), Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling, Chinese Physics B, 22(7), 070502.
  11. [11]  Ghosh, D. $&$ Bhattacharya, S. (2010), Projective synchronization of new hyperchaotic system with fully unknown parameters, Nonlinear Dynamics, 61(1), 11-21.
  12. [12]  Jawaada, W., Noorani, M.S.M., and Al-Sawalha, M.M. (2012), Anti-synchronization of chaotic systems via adaptive sliding mode control, Chinese Physics Letters, 29(12), 120505.
  13. [13]  Kareem, S.O., Ojo, K.S., and Njah, A.N. (2012), Function projective synchronization of identical and non-identical modified finance and Shimizu--Morioka systems, Pramana, 79(1), 71-79.
  14. [14]  Koronovskii, A.A., Moskalenko, O.I., Shurygina, S.A., and Hramov, A.E. (2013), Generalized synchronization in discrete maps. New point of view on weak and strong synchronization. Chaos, Solitons {$\&$ Fractals}, 46, 12-18.
  15. [15]  Li, G.H. (2007), Modified projective synchronization of chaotic system. Chaos, Solitons {$\&$ Fractals}, 32(5), 1786-1790.
  16. [16]  Li, H.L., Jiang, Y.L., and Wang, Z.L. (2015), Anti-synchronization and intermittent anti-synchronization of two identical hyperchaotic Chua systems via impulsive control, Nonlinear Dynamics, 79(2), 919-925.
  17. [17]  Runzi, L. and Yinglan, W. (2012), Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication, Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(2), 023109.
  18. [18]  Runzi, L., Yinglan, W., and Shucheng, D. (2011), Combination synchronization of three classic chaotic systems using active backstepping design. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21(4), 043114.
  19. [19]  Dongmo, E.D., Ojo, K.S., Woafo, P., and Njah, A.N. (2018), Difference synchronization of identical and nonidentical chaotic and hyperchaotic systems of different orders using active backstepping design, Journal of Computational and Nonlinear Dynamics, 13(5).
  20. [20]  Ojo, K.S., Njah, A.N., Olusola, O.I., and Omeike, M.O. (2014), Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique, Nonlinear Dynamics, 77(3), 583-595.
  21. [21]  Sun, J., Shen, Y., Zhang, G., Xu, C., and Cui, G. (2013), Combination--combination synchronization among four identical or different chaotic systems, Nonlinear Dynamics, 73(3), 1211-1222.
  22. [22]  Mahmoud, G.M., Abed-Elhameed, T.M., and Ahmed, M.E. (2016), Generalization of combination--combination synchronization of chaotic n-dimensional fractional-order dynamical systems, Nonlinear Dynamics, 83(4), 1885-1893.
  23. [23]  Sun, J., Shen, Y., Zhang, G., Xu, C., and Cui, G. (2013), Combination--combination synchronization among four identical or different chaotic systems, Nonlinear Dynamics, 73(3), 1211-1222.
  24. [24]  Yadav, V.K., Prasad, G., Srivastava, M., and Das, S. (2019), Combination--combination phase synchronization among non-identical fractional order complex chaotic systems via nonlinear control, International Journal of Dynamics and Control, 7(1), 330-340.
  25. [25]  Sun, J., Shen, Y., Yin, Q., and Xu, C. (2013), Compound synchronization of four memristor chaotic oscillator systems and secure communication, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(1), 013140.
  26. [26]  Sun, J. and Shen, Y. (2016), Compound--combination anti-synchronization of five simplest memristor chaotic systems, Optik, 127(20), 9192-9200.
  27. [27]  Zhang, B. and Deng, F. (2014), Double-compound synchronization of six memristor-based Lorenz systems, Nonlinear Dynamics, 77(4), 1519-1530.

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