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

Mathematics

Muhammad Marwan¹  Muhammad Zainul Abidin¹  Vagner Dos Santos²  Anda Xiong³ 

[1] College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa 84030-900, Paraná, Brazil;School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK;

关键词: nonlinear dynamical systems;    basin of attraction;    chaos;    coexisting attractor;    synchronization;   

DOI  :  10.3390/math10111914

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown