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  • Open Access

Rotation parameter modulation of dynamics in coupled fractional-order Van der Pol oscillators

Zhongkui Sun and Yuqing Lin

Nannan Zhao*

  • *Contact author: nzhao@chd.edu.cn
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Phys. Rev. Research 8, 033160 – Published 10 August, 2026

DOI: https://doi.org/10.1103/jh2w-x92t

Abstract

Traditional fixed-sign coupling schemes impose rigid directional constraints on interaction pathways, while integer-order differential models inherently lack the capacity to describe memory effects and long-range temporal correlations. To overcome these limitations, here we establish a fractional-order coupled Van der Pol oscillator system with a rotation parameter to investigate how the rotation parameter and fractional-order derivative control the dynamics. The rotation parameter distributes the coupling to the x and y variables via trigonometric functions, precisely regulating the sign and weight of coupling in each direction; this governs bifurcations and qualitatively determines the steady-state mode. Moreover, the memory effect of the fractional-order derivative exhibits quadrant dependence: As the fractional-order derivative decreases, the rotation parameter delays amplitude death in the second and third quadrants but accelerates incoherent oscillation death in the fourth quadrant. Finally, employing phase reduction theory, we derive the phase model and numerically verify the system’s transition path. Our findings break away from traditional frameworks, deepen the understanding of fractional-order coupled systems, elucidate the regulatory mechanisms of rotation parameters, and provide a theoretical foundation for controlling synchronization, chimera states, and death states in real-world systems.

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Phys. Rev. Research 8, 033160– Published 10 August, 2026
  • Received 14 April 2026
  • Accepted 20 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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