Higher-order interaction induced chimeralike state in a bipartite network
Rumi Kar1, V K Chandrasekar2, D V Senthilkumar1
1School of Physics, <a href="https://ror.org/01pe3t004">Indian Institute of Science Education and Research</a>, Thiruvananthapuram-695551, Kerala, India.
Physical Review. E
|October 19, 2024
Summary
Higher-order coupling in oscillator networks creates stable chimeralike states by breaking symmetry. This phenomenon depends on interaction types and is suppressed by increased heterogeneity.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Coupled phase oscillators are fundamental to understanding synchronization phenomena.
- Chimeralike states, exhibiting both synchronized and desynchronized behavior, are complex emergent properties in networks.
- Higher-order interactions introduce coupling beyond pairwise connections, potentially altering network dynamics.
Purpose of the Study:
- To investigate the emergence of stable chimeralike states in bipartite networks of coupled phase oscillators.
- To analyze the role of higher-order coupling in breaking the symmetry of homogeneous synchronized states.
- To explore the influence of interaction types (attractive/repulsive) and heterogeneity on chimeralike state formation.
Main Methods:
- Utilizing a bipartite network model of coupled phase oscillators without time delays.
- Applying the Ott-Antonsen ansatz to derive low-dimensional evolution equations for macroscopic order parameters.
- Employing numerical simulations and bifurcation analysis using xppaut to validate theoretical findings.
- Deducing analytical stability conditions for various network states (incoherent, in-phase, out-of-phase synchronized).
Main Results:
- Demonstrated that higher-order coupling induces stable chimeralike states by breaking the symmetry of homogeneous synchronization.
- Identified specific conditions for symmetry breaking: attractive pairwise and repulsive higher-order interactions, or vice versa.
- Showed that increased network heterogeneity suppresses asymmetric chimeralike states, favoring homogeneous symmetric states.
- Confirmed excellent agreement between simulation results and theoretical predictions from derived evolution equations and bifurcation curves.
Conclusions:
- Higher-order coupling is a crucial mechanism for generating complex chimeralike states in oscillator networks.
- The interplay between pairwise and higher-order interactions dictates the manifestation of symmetry-breaking phenomena.
- Network heterogeneity plays a significant role in controlling the stability and prevalence of different collective states.
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