Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network
For researchers studying synchronization in noisy oscillator networks, this provides a theoretical framework for phase-cohesiveness under stochastic uncertainties, though the tree network assumption limits generality.
This paper introduces stochastic phase-cohesiveness for discrete-time Kuramoto oscillators with frequency-dependent coupling in tree networks, deriving sufficient conditions on coupling strength and necessary conditions on sampling period to achieve it. Numerical simulations validate the theoretical results.
This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.