Dynamic, Bifurcation, and Lyapunov Analysis of Fractional Rössler Chaos Using Two Numerical Methods

Reem Allogmany () and S. S. Alzahrani
Additional contact information
Reem Allogmany: Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia
S. S. Alzahrani: Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia

Mathematics, 2025, vol. 13, issue 22, 1-19

Abstract: In this paper, we first used a Modified Numerical Approximation Method (NAM) and then a fractional Laplace Decomposition Method (LDM) to find the solution to the symmetric Rössler attractor. The newly proposed NAM is obtained through a nuanced discretization of the Caputo derivative, rendering it exceptionally effective in emulating the inherent sensitivity and memory-dependent characteristics of fractional-order systems. Second, a comprehensive analysis is conducted to examine how variations in the fractional parameters ρ 1 , ρ 2 , and ρ 3 influence the dynamic response of the system. Third, the simulation results, which include time series, bifurcation diagrams, and Lyapunov exponent spectra, show that the proposed method works well to find changes in system behavior that integer-order or lower-accuracy schemes cannot find. The fractional Laplace Decomposition Method (LDM) is straightforward to implement, computationally efficient, and exhibits outstanding accuracy. Other widely used approximation approaches achieve comparable results. The comparisons between NAM and LDM reveal that these two methodologies are not only highly consistent but also mutually reinforcing. Their straightforward application and robust consistency of numerical solutions indicate that these methods can be effectively utilized in the majority of fractional-order systems, resulting in more accurate and practical answers.

Keywords: fractional systems; Rössler attractor; dynamic analysis; simulations; chaos analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/22/3642/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/22/3642/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:22:p:3642-:d:1793959

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().