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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Chaos in Incommensurate Fractional Order Systems: A Computational Study

Journal of Applied Nonlinear Dynamics 15(4) (2026) 963--978 | DOI:10.5890/JAND.2026.12.011

A. Sai Lekshmi, V. Balakumar

Department of Mathematics, National Institute of Technology Puducherry, Karaikal$-$609 609, India

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Abstract

This article explores the intricate dynamics of incommensurate chaotic systems involving the Caputo fractional derivative as fractional dynamics are particularly suited for capturing complex behaviors in real-world nonlinear systems with memory properties. Initially, we provide Hopf bifurcation analysis which indicates insights into the rich temporal evolution and nonlinear dynamical behavior of these systems. Further, a fractional version of the Runge-Kutta method is employed for the first time to numerically analyze these systems, enabling a thorough investigation of how system parameters and fractional orders influence the emergence and transition of chaos. Numerical simulations, illustrated through phase portraits, reveal the formation of rich chaotic attractors. Additionally, We characterize the systems' stability and chaotic regimes using Lyapunov exponent computations, Poincaré sections, bifurcation diagrams, and maximum Lyapunov exponent spectra.

Acknowledgments

The authors would like to express their sincere gratitude to the anonymous reviewers for their valuable comments and constructive suggestions, which have significantly improved the quality and clarity of the article.

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