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Entropy 2012, 14(9), 1652-1670; doi:10.3390/e14091652
Article

On the Information Transmission Ability of Nonlinear Stochastic Dynamic Networks

*  and
Lab of Control and System Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan
* Author to whom correspondence should be addressed.
Received: 10 August 2012 / Revised: 27 August 2012 / Accepted: 30 August 2012 / Published: 6 September 2012
(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)
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Abstract

The major function of dynamic networks is to sense information from the environment and process the information to the downstream. Therefore how to measure the information transmission ability of a dynamic network is an important topic to evaluate network performance. However, the dynamic behavior of a dynamic network is complex and, despite knowledge of network components, interactions and noises, it is a challenge to measure the information transmission ability of a dynamic network, especially a nonlinear stochastic dynamic network. Based on nonlinear stochastic dynamic system theory, the information transmission ability can be investigated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. To avoid difficulties associated with solving a complex HJI-constrained optimization problem for information transmission ability, the Takagi-Sugeno (T-S) fuzzy model is introduced to approximate the nonlinear stochastic dynamic network by interpolating several local linear stochastic dynamic networks so that a HJI-constrained optimization problem can be replaced by the linear matrix inequalities (LMIs)-constrained optimization problem. The LMI problem can then be efficiently solved for measuring information transmission ability. We found that a more stable (robust) dynamic network has less information transmission ability, and vice versa. Finally, an example of a biochemical network in cellular communication is given to illustrate the measurement of information transmission ability and to confirm the results by using Monte Carlo simulations.
Keywords: information transmission ability; nonlinear stochastic dynamic network; HJI; LMI, T-S fuzzy model; network performance information transmission ability; nonlinear stochastic dynamic network; HJI; LMI, T-S fuzzy model; network performance
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Chen, B.-S.; Lin, Y.-P. On the Information Transmission Ability of Nonlinear Stochastic Dynamic Networks. Entropy 2012, 14, 1652-1670.

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