Hybrid dynamical systems theory and nonlinear dynamical systems over finite fields

The authors study the logic and synchronization characteristics of general dynamical systems called hybrid dynamical systems (HDSs). The proposed theory generalizes the notion of discrete-event dynamical systems by handling numerics as well as symbolics. This theory is supported by the programming language SIGNAL and a mathematical model of relational style. This framework makes it possible to formulate in the same way HDS programming or specification and HDS control. The core of the theory is the notion of HDS resolution, which is based on a reduction technique that maps any HDS specification program into a polynomial dynamical system on the finite field of integers modulo 3; all the algorithms are then based on the study of this dynamical system