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Journal of Applied Mathematics
Volume 2014, Article ID 170748, 7 pages
http://dx.doi.org/10.1155/2014/170748
Research Article

Nonlinear Gossip Algorithms for Wireless Sensor Networks

1School of Telecommunication Engineering, Xidian University, Xian 710071, China
2School of Mechano-Electronic Engineering, Xidian University, Xian 710071, China
3School of Telecommunication Engineering, Guidian University, Guilin 540004, China

Received 22 July 2014; Accepted 20 August 2014; Published 1 September 2014

Academic Editor: Michael Chen

Copyright © 2014 Chao Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study some nonlinear gossip algorithms for wireless sensor networks. Firstly, two types of nonlinear single gossip algorithms are proposed. By using Lyapunov theory, Lagrange mean value theorem, and stochastic Lasalle’s invariance principle, we prove that the nonlinear single gossip algorithms can converge to the average of initial states with probability one. Secondly, two types of nonlinear multigossip algorithms are also presented and the convergence is proved by the same methods. Finally, computer simulation is also given to show the validity of the theoretical results.