Analyzing the relationship between synchronization dynamics in hypernetworks and their single-interaction
Sheida Ansarinasab1, Farnaz Ghassemi1, Fatemeh Parastesh2,3
1Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
Chaos (Woodbury, N.Y.)
|October 24, 2025
Summary
This study analyzes synchronization stability in complex hypernetworks with multiple interaction types. We found nonlinear interactions improve synchronization but increase energy costs, revealing an inverse energy-time relationship for achieving synchrony.
Area of Science:
- Complex Systems and Network Science
- Nonlinear Dynamics and Chaos Theory
- Statistical Physics and Synchronization Phenomena
Background:
- Hypernetworks model systems with simultaneous multi-layer interactions, crucial for understanding collective behaviors like synchronization.
- Existing stability analyses often rely on simplifying assumptions (commuting Laplacians, linear interactions) not representative of real-world systems.
- Analyzing synchronization stability in hypernetworks with non-commuting Laplacians and mixed linear/nonlinear interactions is computationally challenging.
Purpose of the Study:
- To investigate the synchronization dynamics and stability in hypernetworks with non-commuting Laplacians and mixed diffusive coupling functions.
- To develop a method for predicting synchronization stability when direct Master Stability Function (MSF) analysis is intractable.
- To explore the impact of topology (random, ring) and coupling types on synchronization and energy requirements.
Main Methods:
- Investigated hypernetworks with non-commuting Laplacians and both linear and nonlinear diffusive coupling functions on random and ring topologies.
- Established a novel connection between hypernetwork synchronization dynamics and their derived single-interaction counterparts.
- Employed numerical simulations using Lorenz oscillators to validate theoretical predictions and analyze synchronization regions and energy costs.
Main Results:
- Hypernetworks exhibit intermediate synchronization regions influenced by the dominant coupling function.
- Nonlinear interactions enhance synchronizability but lead to higher coupling energy demands.
- An inverse relationship was consistently observed between pre-synchronization coupling energy and the time required to achieve synchronization.
Conclusions:
- The study provides a systematic framework for analyzing synchronization stability in complex hypernetworks with multiple interaction modes.
- The developed method enables qualitative predictions of MSF structure, overcoming limitations of direct analysis.
- Findings offer novel insights into the dynamics, stability, and energy trade-offs of synchronization in realistic complex network systems.
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