Stable Desynchronization for Wireless Sensor Networks: (III) Stability Analysis
Networking and Internet Architecture
2017-04-25 v1
Abstract
In this paper, we use dynamical systems to analyze stability of desynchronization algorithms at equilibrium. We start by illustrating the equilibrium of a dynamic systems and formalizing force components and time phases. Then, we use Linear Approximation to obtain Jaconian (J) matrixes which are used to find the eigenvalues. Next, we employ the Hirst and Macey theorem and Gershgorins theorem to find the bounds of those eigenvalues. Finally, if the number of nodes (n) is within such bounds, the systems are stable at equilibrium. (This paper is the last part of the series Stable Desynchronization for Wireless Sensor Networks - (I) Concepts and Algorithms (II) Performance Evaluation (III) Stability Analysis)
Cite
@article{arxiv.1704.07010,
title = {Stable Desynchronization for Wireless Sensor Networks: (III) Stability Analysis},
author = {Supasate Choochaisri and Kittipat Apicharttrisorn and Chalermek Intanagonwiwat},
journal= {arXiv preprint arXiv:1704.07010},
year = {2017}
}
Comments
21 pages