A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

Abstract

This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines.

Analysis and Applications of the Chaotic Hyperbolic Memristor Model with Fractional Order Derivative

“…As we embark on the next phase of research, the focus will shift towards the deployment and electronic integration of this innovative system, promising new av-enues for exploration in the field of nonlinear dynamical systems. This work lays the groundwork for future research, highlighting the potential for further advancements in the domain of fractional-order chaotic systems and their practical applications.We proposed to compare numerical solutions with other ways [5,33,35] and use this method to solve novel fractional issues [7,9,11,12,14,21,23,25,31,32,34]…”

“…For instance, research documented in [20,22] delves into the applications of fractional calculus to enhance the dynamical range of chaotic systems. Similarly, the works represented by [8,10], along with notable contributions from Hasan et al [24] in the International Journal of Mathematical Engineering and Management Sciences and further studies by Abdoon et al [2] in Mathematical Modelling of Engineering Problems, highlight the advanced mathematical techniques for solving nonlinear differential equations and their pivotal roles in chaos theory. These references collectively underscore the evolving complexity of modelling chaotic systems and the ongoing quest for models that more accurately reflect the multifaceted nature of the universe, thus paving the way for groundbreaking applications in science and engineering.…”

Modeling and analysis of visceral leishmaniasis dynamics using fractional‐order operators: A comparative study

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