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Chimera states on m-directed hypergraphs
Rommel Tchinda Djeudjo1, Timoteo Carletti1, Hiroya Nakao2,3
1University of Namur, Namur Institute for Complex Systems, Department of Mathematics & naXys, B5000 Namur, Belgium.
Physical Review. E
|June 19, 2026
Summary
Chimera states, synchronization patterns with coherent and incoherent regions, emerge more readily in higher-order systems. This study reveals new chimera types in directed hypergraphs due to nonreciprocal interactions.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Chimera states are synchronization patterns with coexisting coherent and incoherent oscillator regions.
- Traditional studies often use symmetric, pairwise network couplings.
- Real-world systems frequently involve nonreciprocal, many-body interactions.
Purpose of the Study:
- Investigate chimera state emergence in nonreciprocal higher-order structures (m-directed hypergraphs).
- Compare chimera states in these structures with their corresponding network counterparts.
- Analyze the impact of directionality and higher-order interactions on chimera formation.
Main Methods:
- Numerical simulations on m-directed hypergraphs and their corresponding networks.
- Comparison of chimera state occurrence across different coupling types (pairwise vs. higher-order, reciprocal vs. nonreciprocal).
- Validation of phase chimera properties using phase reduction theory.
Main Results:
- New types of chimera states emerge in m-directed hypergraphs due to directionality.
- Chimera states are observed over a broader parameter range in higher-order structures compared to networks.
- Directionality and higher-order interactions significantly influence chimera state dynamics.
Conclusions:
- Nonreciprocal higher-order interactions, specifically on m-directed hypergraphs, facilitate the emergence of chimera states.
- The findings highlight the importance of considering network topology and interaction nature (pairwise/higher-order, reciprocal/nonreciprocal) in synchronization studies.
- Phase reduction theory confirms the nature of observed phase chimeras.
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