Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

Muhammad Marwan, Vagner Dos Santos, Muhammad Zainul Abidin and Anda Xiong
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Muhammad Marwan: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Vagner Dos Santos: Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa 84030-900, Paraná, Brazil
Muhammad Zainul Abidin: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Anda Xiong: School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK

Mathematics, 2022, vol. 10, issue 11, 1-15

Abstract: This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different basins, several approaches such as bifurcation diagrams, Lyapunov exponents, and the Poincaré section are applied. The second half of the study synchronizes two mechanical chaotic systems using a novel controller, with gyrostat and quadrotor unmanned aerial vehicle (QUAV) chaotic systems acting as master and slave systems, respectively. The error dynamical system and the parameter updated law are built using Lyapunov’s theory, and it is discovered that under certain parametric conditions, the trajectories of the QUAV chaotic system overlap and begin to match the features of the gyrostat chaotic system.

Keywords: nonlinear dynamical systems; basin of attraction; chaos; coexisting attractor; synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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