On the Information Transmission Ability of Nonlinear Stochastic Dynamic Networks

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.