Title: Stable Desynchronization for Wireless Sensor Networks: (III) Stability Analysis,
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)