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Amplitude death in delay-coupled complex networks with higher-order interactions.
Rui Xiao1, Xueli Wang1, Donghua Zhao2
1China University of Mining and Technology, School of Mathematics, Xuzhou 221008, China.
Physical Review. E
|November 18, 2025
Summary
Higher-order interactions in complex networks significantly influence oscillatory dynamics and amplitude death (AD). Increased interaction strengths reduce AD, while denser networks promote oscillations, offering insights into complex system control.
Area of Science:
- Complex Systems
- Network Science
- Nonlinear Dynamics
Background:
- Oscillatory phenomena are crucial in diverse fields like biology and engineering.
- Higher-order networks, involving interactions among three or more units, offer a more realistic model for complex systems.
- The impact of these higher-order interactions on amplitude death (AD) is not well understood.
Purpose of the Study:
- Investigate amplitude death (AD) in complex networks with delayed coupling.
- Analyze the effects of first-order, second-order, and combined interaction schemes.
- Understand how higher-order interactions modulate oscillatory behavior and AD.
Main Methods:
- Utilized a dimensionality reduction approach to simplify high-dimensional systems.
- Analytically derived the boundaries of the amplitude death region.
- Employed numerical simulations to validate the theoretical findings.
Main Results:
- Both first-order and second-order interaction strengths, along with network topology, significantly affect oscillations.
- Increased interaction strengths decrease the AD region, leading to sequential or direct transitions between oscillation and AD.
- Higher connection density promotes oscillations, whereas sparser connectivity favors the AD state.
Conclusions:
- Higher-order interactions play a critical role in shaping oscillatory dynamics and amplitude death in complex networks.
- Findings provide a deeper understanding of controlling and modulating oscillations in engineered and natural systems.
- The study highlights the importance of network structure and interaction complexity in emergent dynamics.
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