Stability and bifurcation of a time-delayed fractional three-disk system

Elham Ghafari, Reza Khoshsiar Ghaziani, Javad Alidousti and Khayyam Salehi

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 243, issue C, 16-34

Abstract: This study investigates a fractional-order three-disk dynamo system incorporating time delay and viscous friction, enhancing its relevance to real-world phenomena. We analyze dynamics of the system with and without time delay, revealing richer behaviors in the delayed case. Through theoretical analysis, we investigate equilibrium points and their stability, identifying pitchfork and double-Hopf bifurcations that lead to complex dynamics, including three-dimensional torus structures. Numerical simulations validate these findings for both fractional and classical systems, highlighting the impact of fractional-order derivatives and time delays. A comparative analysis shows that the fractional-order system exhibits a broader stability region than its integer-order counterpart, underscoring the stabilizing role of fractional calculus. These results provide insights into modeling magnetic field dynamics in geophysical and astrophysical systems, with potential applications to geomagnetic reversals and stellar magnetic cycles.

Keywords: Three-disk dynamo; Fractional differential equations; Time delay; Stability analysis; Hopf bifurcation (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:243:y:2026:i:c:p:16-34

DOI: 10.1016/j.matcom.2025.11.023

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