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International Workshop on Interacting Particle Systems

Emergent Behaviors of Thermomechanical Kuramoto Ensemble on a Ring Lattice


Seung-Yeal Ha , Seoul National University, Korea


29 Mar, 10:05 - 10:35


The temporal evolution of thermomechanical Kuramoto oscillators often appears in biological oscillator ensemble. In this talk, we propose a new generalized thermomechanical Kuramoto model on a ring lattice. Our proposed model is derived from the thermodynamic Cucker-Smale model for flocking on the 2D free space under the assumption that the ration between velocity field and temperature field at each lattice point has a uniform magnitude. The proposed model satisfies an entropy principle and exhibits emergent dynamics under some sufficient frameworks formulated in terms of initial data and system parameters. Moreover, the phase field tends to the Kuramoto phase field time-asymptotically.