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First-order transition to oscillation death in coupled oscillators with higher-order interactions
Richita Ghosh1, Umesh Kumar Verma2, Sarika Jalan2
1Department of Physics, Central University of Rajasthan, Rajasthan, Ajmer-305 817, India.
Physical Review. E
|November 18, 2023
Summary
Higher-order interactions in coupled Stuart-Landau oscillators lead to explosive transitions and multiple steady states. This contrasts with pairwise interactions, offering insights into complex systems dynamics.
Area of Science:
- Complex Systems Dynamics
- Nonlinear Oscillators
- Network Science
Background:
- Stuart-Landau oscillators are fundamental models for studying synchronization phenomena.
- Coupling through conjugate or dissimilar variables and higher-order interactions are crucial in real-world complex systems.
- Simplicial complexes provide a framework for analyzing networks with higher-order structures.
Purpose of the Study:
- To investigate the dynamical evolution of globally coupled Stuart-Landau oscillators on simplicial complexes.
- To explore the impact of higher-order (triadic) interactions versus pairwise (dyadic) interactions on system dynamics.
- To analyze the emergence of phase transitions and steady states in these complex networks.
Main Methods:
- Numerical simulations of globally coupled Stuart-Landau oscillators on simplicial complexes.
- Analysis of phase transitions, specifically focusing on the order of the transition (first-order vs. second-order).
- Analytical calculation of the backward transition point to understand dynamical state origins.
Main Results:
- A first-order explosive phase transition from oscillation to oscillation death was observed with triadic interactions.
- Higher-order interactions resulted in four distinct homogeneous steady states, compared to two with dyadic interactions.
- The observed dynamical states and transition behaviors were robust against noise.
Conclusions:
- Higher-order interactions fundamentally alter the collective dynamics of coupled oscillators, leading to explosive transitions and richer steady-state behavior.
- The findings provide a deeper understanding of complex systems with intricate interaction structures, applicable to fields like ecology and epidemiology.
- The analytical framework developed aids in characterizing dynamical states within transition regions of complex networks.
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