Analyzing chaotic systems with multi-step methods: Theory and simulations

Analyzing chaotic systems with multi-step methods: Theory and simulations

Identifying and analyzing fixed points plays a crucial role in chaos theory for grasping the system behavior and advancing the understanding of its fundamental mechanics. This study explores new chaotic nonlinear integro-differential systems with four variables, employing Caputo–Fabrizio and Atangan...

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Bibliographic Details
Main Authors: Meriem Mansouria Belhamiti, Zoubir Dahmani, Jehad Alzabut, D.K. Almutairi, Hasib Khan
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Alexandria Engineering Journal
Subjects:
Caputo–Fabrizio derivative
Atangana–Baleanu derivative
Fixed point theorem
Ulam–Hyers stability
Three-step Adams–Bashforth scheme
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016824014145
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Summary:Identifying and analyzing fixed points plays a crucial role in chaos theory for grasping the system behavior and advancing the understanding of its fundamental mechanics. This study explores new chaotic nonlinear integro-differential systems with four variables, employing Caputo–Fabrizio and Atangana–Baleanu derivatives. We confirm the presence and reliability of solutions and offer a real-life example. Additionally, we implement the suggested multi-step techniques on different nonlinear chaotic systems to demonstrate their accuracy.
ISSN:1110-0168

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