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Effective-frequency shear organizes chaotic response under higher-order coupling
1College of Future Information Technology, Fudan University, Shanghai 200438, China.
Chaos (Woodbury, N.Y.)
|July 22, 2026
Summary
Higher-order interactions in chaotic systems are better explained by effective-frequency shear than phase coherence. This shear, driven by amplitude heterogeneity, offers a new pathway for controlling chaotic dynamics.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Theoretical physics
Background:
- Understanding how higher-order interactions influence chaotic dynamics is crucial.
- Current models often rely on phase coherence, which is insufficient to explain collective instability.
- Amplitude-active systems require a deeper look beyond simple coherence.
Purpose of the Study:
- To investigate the role of higher-order interactions in reorganizing chaotic responses.
- To explore mechanisms beyond phase coherence in coupled oscillator systems.
- To establish a new framework for understanding chaotic dynamics control.
Main Methods:
- Studied a minimal globally coupled quartet of nonisochronous Stuart-Landau oscillators.
- Incorporated pairwise and symmetric three-body interactions.
- Analyzed the system's dynamics focusing on effective-frequency shear and amplitude heterogeneity.
Main Results:
- Higher-order coupling reconstructs, rather than creates, irregular dynamics.
- Effective-frequency shear, not phase coherence, organizes the chaotic response reconstruction.
- Amplitude heterogeneity is regulated by higher-order coupling and converted to shear by nonisochronicity.
Conclusions:
- A reduced shear-based description effectively explains higher-order control of chaotic dynamics.
- An indirect amplitude-shear pathway is identified for controlling chaotic behavior.
- This work provides a novel perspective on complex system dynamics and stability.
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