Decomposition of admissible functions in weighted coupled cell networks

This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. Currently, the concept of an admissible function is defined through a very high-level description, with the shortcoming of being difficult to verify or design such a function. We introduce two decompositions in order to have a low-level representation of the underlying mathematical object. The first one is the more intuitive one and it solves the verification problem. More importantly, it provides us with essential definitions that prove crucial in order to define the second decomposition. The second decomposition is both verification and design friendly. Although this second decomposition only gives an equivalent representation under certain assumptions, it still proves to be a valid design tool even when they do not apply.