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Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation
1Department of Mathematics, National Institute of Technology, Durgapur 713209, India.
Chaos (Woodbury, N.Y.)
|February 3, 2019
Summary
We found that partial degree-frequency correlation in complex networks can enhance explosive synchronization (ES). This phenomenon, observed in scale-free and random networks, was also seen in a real biological network.
Area of Science:
- Complex networks
- Nonlinear dynamics
- Statistical physics
Background:
- The Sakaguchi-Kuramoto (SK) model is a fundamental tool for studying synchronization phenomena in coupled oscillator systems.
- Synchronization transitions in networks are influenced by node properties like degree and natural frequencies.
- Explosive synchronization (ES) is a sudden transition to a synchronized state, often observed under specific network conditions.
Purpose of the Study:
- To analytically and numerically investigate the transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks.
- To explore the impact of partial degree-frequency correlation on synchronization dynamics.
- To identify conditions favoring explosive synchronization (ES) in different network topologies.
Main Methods:
- Analytical derivation of self-consistent equations for critical coupling strength (λc) and group angular velocity (Ωc) in the thermodynamic limit.
- Numerical simulations of the SK model on scale-free (SF) and Erdős-Rényi (ER) networks.
- Systematic variation of the fraction (f) of nodes with degree-correlated frequencies and the phase frustration parameter (α).
Main Results:
- Explosive synchronization (ES) was observed in both SF and ER networks under partial degree-frequency correlation.
- For SF networks with scaling exponent γ<3, partial correlation (10%≤f≤70%) significantly broadens the parameter range for ES compared to full correlation.
- ES was also observed in SF networks with γ>3, a regime where it's absent in fully correlated systems. ER networks showed ES within a narrow α window for 30%≤f≤50%.
- Analytical predictions for critical coupling strength closely matched numerical results across all investigated scenarios.
- ES was demonstrated in the metabolic network of *Caenorhabditis elegans*, confirming findings in a real-world biological system.
Conclusions:
- Partial degree-frequency correlation is a crucial factor in promoting and broadening the parameter space for explosive synchronization in complex networks.
- The findings highlight the importance of considering heterogeneous frequency distributions and degree correlations for understanding synchronization phenomena.
- The observation of ES in a biological network suggests potential implications for understanding coordinated dynamics in biological systems.
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