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Rewriting system (RS) are a formalism widely used in computer science. However, such a formalism can also be used to specify executable models of dynamical systems (DS) by allowing the specification of the evolution laws of the systems in a local manner. The main drawback of RS is that they are well understood and well known only for terms (a tree-like structure) and that their expressivity is not enough for the representation of complex organizations that can be found in DS. We propose a framework based on topological notion to extend the notion of RS on more sophisticated structures; the corresponding concepts are validated through the development of an experimental programming language, MGS, dedicated to the simulation of DS. We show how the MGS rewriting system can be used to specify complex dynamical systems and illustrate it with the simulation of the motility of the nematode's sperm cell.

Using Rewriting Techniques in the Simulation of Dynamical Systems: Application to the Modeling of Sperm Crawling