{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:11Z","timestamp":1760243711977,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2012,9,6]],"date-time":"2012-09-06T00:00:00Z","timestamp":1346889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e14091652","type":"journal-article","created":{"date-parts":[[2012,9,6]],"date-time":"2012-09-06T11:08:30Z","timestamp":1346929710000},"page":"1652-1670","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the Information Transmission Ability of Nonlinear Stochastic Dynamic Networks"],"prefix":"10.3390","volume":"14","author":[{"given":"Bor-Sen","family":"Chen","sequence":"first","affiliation":[{"name":"Lab of Control and System Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying-Po","family":"Lin","sequence":"additional","affiliation":[{"name":"Lab of Control and System Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Klipp, E. 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