Asynchronous and synchronous states in the heterogeneous Kuramoto model

• Applicant: Dr. Yagmur Kati
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Theoretical Condensed Matter Physics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 506198590

Synchronization of interacting oscillators is a ubiquitous phenomenon found in many physical, chemical, and biological systems, which emerges when the attractive coupling between the oscillators is strong enough to overcome the disparity in their natural frequencies or other heterogeneities. Most studies of coupled-oscillator systems considered the randomness only in the distribution of the frequencies, not in the manner of interactions, despite its importance and unavoidability in many real systems: for real systems, it is plausible, that the coupling strengths between individual units are subject to a certain degree of disorder. Besides the network noise generated by this disorder in coupling, inertia is another factor that diminishes the synchronization and may lead to an asynchronous state. A good understanding of the asynchronous state is crucial since it is encountered in many systems, for instance, in neurons in cortical brain regions in awake behaving animals or in muscles of insects; asynchronous states are also responsible for widespread blackouts in large power grid networks. We will study the heterogeneous network problem from the perspective of asynchrony with and without inertial effects. We will derive equations for the second-order temporal correlation statistics, and solve them in order to obtain the self-consistent autocorrelation functions of the network fluctuations and of the oscillators.

• DFG Programme: WBP Position