Projecting dynamical systems via a support bound

Abstract: For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate (in other words, projecting the system on the coordinate). This problem can be viewed as a special case of the general elimination problem for systems of differential equations and appears in applications to modeling and control. We give a bound for the Newton polytope of such minimal equation and show that our bound is sharp in "more than half of the cases". We further use this bound to design an algorithm for computing the minimal equation following the evaluation-interpolation paradigm. We demonstrate that our implementation of the algorithm can tackle problems which are out of reach for the state-of-the-art software for differential elimination.