Open Access

ARTICLE

Synchronization Phenomena Investigation of a New Nonlinear Dynamical System 4D by Gardano’s and Lyapunov’s Methods

by Abdulsattar Abdullah Hamad¹, Ahmed S. Al-Obeidi², Enas H. Al-Taiy², Osamah Ibrahim Khalaf³, Dac-Nhuong Le^4,5,*

1 School of Mathematics, Madurai Kamaraj University, Madurai, 625021, India
2 Specialty of Mathematics, Gifted School of Nineveh, Mosul, Iraq
3 Al-Nahrain University, Baghdad, 70030, Iraq
4 Institute of Research and Development, Duy Tan University, Danang, 550000, Vietnam
5 Faculty of Information Technology, Duy Tan University, Danang, 550000, Vietnam

* Corresponding Author: Dac-Nhuong Le. Email:

Computers, Materials & Continua 2021, 66(3), 3311-3327. https://doi.org/10.32604/cmc.2021.013395

Received 05 August 2020; Accepted 07 September 2020; Issue published 28 December 2020

Abstract

Synchronization is one of the most important characteristics of dynamic systems. For this paper, the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems. The findings have allowed authors to develop two analytical approaches using the second Lyapunov (Lyp) method and the Gardano method. Since the Gardano method does not involve the development of special positive Lyp functions, it is very efficient and convenient to achieve excessive system SYCR phenomena. Error is overcome by using Gardano and overcoming some problems in Lyp. Thus we get a great investigation into the convergence of error dynamics, the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them, an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization, by making use of the Lyapunov expansion analysis, a proposed control method is developed to determine the actual. The basic idea in the proposed way is to receive the evolution of between two methods. Finally, the present model has been applied and showing in a new attractor, and the obtained results are compared with other approximate results, and the nearly good coincidence was obtained.

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