Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network

Matin Jafarian; Mohammad H. Mamduhi; Karl H. Johansson

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arXiv · 1903.09676

Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network

Matin Jafarian·Mohammad H. Mamduhi·Karl H. Johansson

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Abstract

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.

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BibTeX RIS

Matin Jafarian, Mohammad H. Mamduhi, Karl H. Johansson. 2019-03-22. Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network. https://arxiv.org/abs/1903.09676

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