We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.
We analytically obtain the one
Dimensional effective interaction constant in term of three dimensional s-wave
Scattering length and extract the confinementinduced resonance condition. The
Universal scattering amplitude indicates the occurrence of the confinement
Induced resonance (CIR)....
Examine the joint effect of small scale fading and propagation path loss. Also,
We study cooperation in application to finite networks, i.e. when the number of
Cooperating nodes is small. Stochastic geometry and order statistics are used
To develop analytical models that tightly match the simulat...
We prove that for all pairs of primitive Pisot or uniform
Substitutions with the same dominating eigenvalue, there exists a finite set of
Block maps such that every block map between the corresponding subshifts is an
Element of this set, up to a shift. This result is proved using a common
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