Computability of analogue networks

We define a general concept of a network of analogue modules connected by channels, processing data from a metric space A, and operating with respect to a global continuous clock . The inputs and outputs of the network are continuous streams u : → A, and the input-output behaviour of the network with system parameters from A is modelled by a function Φ : C[ , A]×A → C[ , A] (p, q > 0, r ≥ 0), where C[ , A] is the set of all continuous streams equipped with the compact-open topology. We give an equational specification of the network, and a semantics which involves solving a fixed point equation over C[ , A] using a contraction principle. We analyse two case studies involving mechanical systems. Finally, we introduce a custom-made concrete computation theory over C[ , A] and show that if the modules are concretely computable then so is the function Φ.