Hysteretic behavior of spatially coupled phase-oscillators

¹ MTA-BME Morphodynamics Research Group, Budapest, Hungary.
² Department of Mechanics, Materials and Structures, Faculty of Architecture, Budapest University of Technology and Economics, Budapest, Hungary.
³ Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, Budapest, Hungary.
⁴ Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, Hungary.

^* Corresponding author: toth.balazs@epito.bme.hu

Received: 15 January 2019
Accepted: 25 June 2019

Abstract

Motivated by phenomena related to biological systems such as the synchronously flashing swarms of fireflies, we investigate a network of phase oscillators evolving under the generalized Kuramoto model with inertia. A distance-dependent, spatial coupling between the oscillators is considered. Zeroth and first order kernel functions with finite kernel radii were chosen to investigate the effect of local interactions. The hysteretic dynamics of the synchronization depending on the coupling parameter was analyzed for different kernel radii. Numerical investigations demonstrate that (1) locally locked clusters develop for small coupling strength values, (2) the hysteretic behavior vanishes for small kernel radii, (3) the ratio of the kernel radius and the maximal distance between the oscillators characterizes the behavior of the network.