Irreducibility, reduction and transfer equivalence of nonlinear input–output equations on homogeneous time scales

The purpose of this paper is to present a necessary and sufficient condition for irreducibility of nonlinear input–output delta differential equations. The condition is presented in terms of the common left divisor of two differential polynomials describing the behaviour of the system defined on a homogenous time scale. The concept of reduction is explained. Subsequently, the definition of transfer equivalence based upon the notion of an irreducible differential form of the system is introduced, inspired by the analogous definition for continuous-time systems.