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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

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

Journal of Applied Nonlinear Dynamics 12(4) (2023) 799--813 | DOI:10.5890/JAND.2023.12.012

Rami Amira, Fareh Hannachi

Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University-

Tebessa, Algeria

Echahid Cheikh Larbi Tebessi University - Tebessa, Algeria

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Abstract

This research paper studies a new chaotic system modified from Lorenz system. Firstly, the stability of the fixed points are studied. then, the dynamics of the novel system are investigated using bifurcations diagrams, Lyapunov exponents, 0-1 test, as well as Poincare sections. Furthermore, we use the three previously mentioned methods and see how our system exhibit a chaotic behavior from doubling of period. In addition to that, comparison of our proposed system with 30 other systems are implemented in order to see their advantage in secure communication using Kaplan-York dimension. In the second part of this paper, we implement an identical synchronization in less than $0.4$ seconds via an adaptive control law. Moreover, any results we get analytically will be checked by Matlab simulation.

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