SECURE COMMUNICATION USING THE SYNCHRONIZATION OF TWO FRACTIONAL-ORDER CHAOTIC SYSTEMS WITH ORDER CHANGES USING THE FINITE-TIME OPTIMAL CONTROL APPROACH

Authors:

Ali Soleimanizadeh,Mohammad Ali Nekui,

DOI NO:

https://doi.org/10.26782/jmcms.2021.10.00009

Keywords:

Fractional calculus,Secure communication,Chaotic masking,

Abstract

In this paper synchronization problem for two different fractional-order chaotic systems has been investigated. Based on fractional calculus, optimality conditions for this synchronization have been achieved. Synchronization Time and control signals are two factors that are optimized. After that, the synchronization method is applied in secure communication. Finally using the simulation example, the performance of the proposed method for synchronization and chaotic masking is shown.

Refference:

I. A. A. Koronovskii, O. I. Moskalenko, and A. E. Hramov: On the use of chaotic synchronization for secure communication. Physics-Uspekhi 52 (2009), 12131238.
II. Awad El-Gohary, Optimal synchronization of Rssler system with complete uncertain parameters, Chaos, Solitons and Fractals, Volume 27, Issue 2, January 2006, Pages 345-355, ISSN 0960-0779.
III. Foroogh Motallebzadeh, Mohammad Reza Jahed Motlagh, Zahra Rahmani Cherati, Synchronization of different-order chaotic systems: Adaptive active vs. optimal control, Communications in Nonlinear Science and Numerical Simulation, Volume 17, Issue 9, September 2012, Pages 3643-3657, ISSN 1007-5704.
IV. G. Peng, Y. Jiang, F. Chen, ”Generalized projective synchronization of fractional order chaotic systems”, Phys. A 387 (2008) 37383746.
V. Ge Z, Yi C. ”Chaos in a nonlinear damped Mathieu system in a nano resonator system and in its fractional order systems”. Chaos Soliton Fract 2007;32(1):4261.
VI. Jian-Bing Hu, Guo-Ping Lu, Shi-Bing Zhang, Ling-Dong Zhao , Lyapunov stability theorem about fractional system without and with delay, 20 (2015) 905-913.
VII. K. B. Arman, K. Fallahi, N. Pariz, and H. Leung: A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Comm. Nonlinear Sci. Numer. Simul. 14 (2009), 863879.
VIII. L. A. B. Torres and L. A. Aguirre: Transmitting information by controlling nonlinear oscillators. Physica D 196 (2004), 387406.
IX. L.M. Pecora, T.L. Carroll, ”Synchronization in chaotic systems”, Phys. Rev. Lett. 64 (1990) 821824.
X. Lin Pan , Wuneng Zhou b, Long Zhou a, Kehui Sun ”Chaos synchronization between two different fractional-order hyperchaotic systems”. Commun Nonlinear Sci Numer Simulat 16 (2011) 26282640
XI. M. J. Chen, D. P. Li, and A. J. Zhang: Chaotic synchronization based on nonlinear state observer and its application in secure communication. J. Marine Sci. Appl. 3 (2004), 6470.
XII. M.S.Tavazoei,M.Haeri, A necessary condition for double scroll attractor existence in fractional-order systems, Physics Letters A367(2007)102113.
XIII. Manabe, S., Early development of fractional order control, DETC2003/VIB-48370, in Proceedings of DETC03, ASME 2003 Design Engineering Technical Conference, Chicago, Illinois, September 26, 2003.
XIV. Momani S, Odibat Z. ”Numerical comparison of methods for solving linear differential equations of fractional order”. Chaos Soliton Fract 2007;31(5):124855.
XV. Odibat ZM, Momani S. ”Application of variational iteration method to nonlinear differential equations of fractional order”.Int J Nonlinear Sci Numer Simul 2006;7(1):2734
XVI. R. M. Guerra and W. Yu: Chaotic synchronization and secure communication via sliding mode observer. Internat. J. Bifurcation Chaos 18 (2008), 235243.
XVII. T.E. Duncan, Y. Hu and B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion, I. Theory, SIAM J. Control Optim. 38 (2000) 582-612.
XVIII. Y. Hu and B. ksendal, Fractional white noise calculus and applications to finance, Infinite Dim. Anal. Quantum Probab. Related Topics 6 (2003), 1-32.

View Download