We present a new hydrodynamic model for synchronization phenomena which is a type of pressureless Euler system with nonlocal interaction forces. This system can be formally derived from the Kuramoto model with inertia, which is a classical model of interacting phase oscillators widely used to investigate synchronization phenomena, through a kinetic description under the mono-kinetic closure assumption. For the proposed system, we first establish local-in-time existence and uniqueness of classical solutions. For the case of identical natural frequencies, we provide synchronization estimates under suitable assumptions on the initial configurations. We also analyze critical thresholds leading to finite-time blow-up or global-in-time existence of classical solutions. In particular, our proposed model exhibits the finite-time blow-up phenomenon, which is not observed in the classical Kuramoto models, even with a smooth distribution function for natural frequencies. Finally, we numerically investigate synchronization, finite-time blow-up, phase transitions, and hysteresis phenomena.
|Number of pages||53|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2020 Oct 1|
Bibliographical noteFunding Information:
YPC was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918) and POSCO Science Fellowship of POSCO TJ Park Foundation.
© 2020 World Scientific Publishing Company.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics