Stochastic π-calculus for describing dynamics of spatially extended systems: system specifications for simulations of pattern formations in biological systems

摘要

There exist some theories for modelling computer and communication network systems. The r-calculus, proposed by Robin Milber, provides an algebraic method for modelling mobile processes exhibited in such systems. Therefore, this theory is especially suitable to describe complex and complicated systems, in which the structure of interactions among constituents will dynamically change. In order to describe spatial dynamical structures (often observed in biological systems), we introduced probabilities which are dependent on systems parameters including spatial coordinates of constituents of the system concerned.