Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically pre-determined what signal channels are inputs and what are outputs. These models do not capture the practical need to incorporate different experimental situations, where different selections of input and output channels are applied to the same network. Moreover, a unified view of different network models is lacking. This work makes an initial step towards addressing the above issues by taking a behavioral perspective, where input and output channels are not pre-determined. The focus of this work is on behavioral network models with only external variables. By exploiting the concept of hypergraphs, novel dual graphical representations, called system graphs and signal graphs, are introduced for behavioral networks. Moreover, connections between behavioral network models and structural vector autoregressive models are established. In addition to their connections in graphical representations, it is shown that the regularity of interconnections is an essential assumption when choosing a structural vector autoregressive model.

Multifunctional intrinsic self-healing polymers (ISP) are gaining increasing attention these days, and many studies have been devoted to solving the conflict between achieving high mechanical polymer strength and active polymer chain diffusion. In this research, we developed an optimized self-healing composite coating by adding Benzotriazole (BTA) loaded nano silica (SiO₂@BTA) to a dynamic cross-linked Polydimethylsiloxane (PDMS) network，which allows substantial and fast healing of the material integrity upon damage due to the hydrogen interaction between urea and BTA. BTA leaching tests demonstrated a longer release profile during the coating service life and corrosion tests in a 3.5 wt% NaCl aqueous solution indicated that the SiO₂@BTA modified PDMS coating shows enhanced corrosion protection of carbon steel upon coating damage. Moreover, after addition of SiO₂@BTA, the material failure strength increased from ~1.5 MPa to ~5.5 MPa, and the healing efficiency increased from ~59% to ~90% for 24 h healing at room temperature. Above all, this research provides an intrinsic self-healing coating design method to improve the mechanical strength and the self-healing ability of the ISP as well as enhancing the coating's corrosion protection ability.