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

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.

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

“…Similarly, the work of Iqbal et al [12,13] verifies the existence of chaos and controllability in Cancer systems, revealing additional applications of chaos in biological systems. Apart from the field of biological sciences, the term chaos has a variety of contribution in the applications of robotics [25,31] and engineering [26,37] as well.…”

“…Similarly, Sprott and Xiong [41] classified basins of attraction in a variety of scenario and later investigated basins of tri-stability [46] for the first time in the Lorenz system to gain more insight and detail. In 2022, Marwan et al [26] utilized the same method for locating basins in a mechanical-based system and discussed its basin in two and three dimensions.…”

Generalized external synchronization of networks based on clustered pandemic systems—The approach of Covid-19 towards influenza

“…In the beginning it was also linked with the butterfly effect. Several researchers used chaos as a positive term in their fields and have showed variety of its applications such as in engineering [ 16 , 17 ], secure communication [ 18 , 19 ], biology [ 20 , 21 ] and reference therein. But, in comparison with the importance of human lives, the term chaos is more dangerous.…”

A New DC Offset Boostable Chaotic System with Multistability, Coexisting Attractors and Its Adaptive Synchronization

“…In [47], three different attractors are generated based on the equilibrium and initial conditions. This initial condition-based multiple attractor behavior is realized in many chaotic systems such as Gyrostat system [48], memristive system [49], unified system [50], conservative system [51], neuron system [52] and chemical oscillator [53] etc.…”