• Corpus ID: 10424273

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

@article{Choochaisri2017StableDF,
  title={Stable Desynchronization for Wireless Sensor Networks: (III) Stability Analysis},
  author={Supasate Choochaisri and Kittipat Apicharttrisorn and Chalermek Intanagonwiwat},
  journal={ArXiv},
  year={2017},
  volume={abs/1704.07010}
}
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… 

Figures from this paper

References

SHOWING 1-6 OF 6 REFERENCES
Toeplitz and Circulant Matrices: A Review
  • R. Gray
  • Mathematics
    Found. Trends Commun. Inf. Theory
  • 2005
TLDR
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toepler matrices with absolutely summable elements are derived in a tutorial manner in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject.
Bounding the Roots of Polynomials
TLDR
This note will show one method of finding bounds for any possible root of a polynomial, then state the bounds as a theorem, give some examples on how the theorem is used, and give the proof of the theorem.
A Geometric Interpretation of the Solution of the General Quartic Polynomial
where each of the ai's is a rational number and a, is not zero. We might ask if the solutions of this equation can be expressed in terms of the coefficients aO, . . ., a, using only the operations of
Gershgorins theorem for estimating eigenvalues
  • 2012
Uber die abgrenzung der eigenwerte einer matrix
  • Bulletin de l’Academie des Sciences de l’URSS. Classe des Sciences Mathematiques et na,
  • 1931