Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication

Smail Kaouache

doi:10.32323/ujma.739649

EN

Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication

Abstract

In this paper, we propose a new approach to investigate the chaos projective synchronization of the modified fractional-order hyperchaotic Rossler system and its application in secure communication. The proposed communication system consists of four main elements including: modulation, master system, slave system and demodulation. The main idea of this approach is to inject the bounded or unbounded message into one of the parameters of the proposed system using the exponential function. However, the way of injecting the message in the modulation parameter must not remove the hyperchaotic character of the signal sent to the slave system. The slave system adaptively synchronizes with the master system, and the information signal can be recovered. Based on the Lyapunov stability theory, an adaptation laws and adaptive control are designed to achieve projection synchronization of the modified system. Numerical simulations are performed to show the feasibility of the proposed secure communication scheme.

Keywords

Adaptative control , Chaotic systems , Fractional-order , Lyapunov stability , Projective synchronization

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Smail Kaouache ^*
0000-0001-7231-9422
Algeria

Publication Date

June 30, 2021

Submission Date

May 19, 2020

Acceptance Date

June 18, 2021

Published in Issue

Year 2021 Volume: 4 Number: 2

DOI

https://doi.org/10.32323/ujma.739649

IZ

https://izlik.org/JA84ZK95EL

APA

Kaouache, S. (2021). Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication. Universal Journal of Mathematics and Applications, 4(2), 50-58. https://doi.org/10.32323/ujma.739649

AMA

1.Kaouache S. Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication. Univ. J. Math. Appl. 2021;4(2):50-58. doi:10.32323/ujma.739649

Chicago

Kaouache, Smail. 2021. “Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication”. Universal Journal of Mathematics and Applications 4 (2): 50-58. https://doi.org/10.32323/ujma.739649.

EndNote

Kaouache S (June 1, 2021) Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication. Universal Journal of Mathematics and Applications 4 2 50–58.

IEEE

[1]S. Kaouache, “Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication”, Univ. J. Math. Appl., vol. 4, no. 2, pp. 50–58, June 2021, doi: 10.32323/ujma.739649.

ISNAD

Kaouache, Smail. “Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication”. Universal Journal of Mathematics and Applications 4/2 (June 1, 2021): 50-58. https://doi.org/10.32323/ujma.739649.

JAMA

1.Kaouache S. Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication. Univ. J. Math. Appl. 2021;4:50–58.

MLA

Kaouache, Smail. “Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication”. Universal Journal of Mathematics and Applications, vol. 4, no. 2, June 2021, pp. 50-58, doi:10.32323/ujma.739649.

Vancouver

1.Smail Kaouache. Projective Synchronization of The Modified Fractional-Order Hyperchaotic R\"{o}ssler System and Its Application in Secure Communication. Univ. J. Math. Appl. 2021 Jun. 1;4(2):50-8. doi:10.32323/ujma.739649