Statistical and Dynamical Analysis of Hidden Attractors in the Fractional Glukhovsky–Dolzhansky System

Fractal and Fractional 2026 Open access

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Authors: Salem Mubarak Alzahrani, Ghaliah Alhamzi, Mona Bin-Asfour, Mansoor Alsulami, Khdija O. Taha, Najat Almutairi, Sayed Saber
DOI: 10.3390/fractalfract10060377
Cited by: 1
References: 57

Abstract

This study investigates the reliable numerical analysis of chaotic dynamics in the Glukhovsky–Dolzhansky system, which models convective fluid motion in a rotating ellipsoidal cavity. Hidden and self-excited attractors are localized using the numerical continuation method (NCM), Pyragas time-delayed feedback control, and Leonov’s analytical dimension formula following global stability loss. A critical assessment of Lyapunov exponents and Lyapunov dimensions in a finite-time setting shows that positive values over long but finite intervals may incorrectly indicate sustained chaos due to transient effects and shadowing breakdown. Furthermore, we demonstrate that the fractional order γ plays a bidirectional control role: it induces chaotic behavior at ρ=5 for γ

Fields of Study & Subjects

Chaos control and synchronization stochastic dynamics and bifurcation Quantum chaos and dynamical systems

Publication details

Journal / source
Fractal and Fractional
Publisher
MDPI AG
Volume
10
Issue
6
Pages
377–377
Publication date
30 May 2026
Language
EN