Discrete multiple delay advection–reaction operators

In this work we introduce a multiple delay term to the family of discrete operators known as advection–reaction operators. We present detailed quantitative information of the delay inclusion on the dynamics of the discrete dynamical systems with iteration functions given by the advection–reaction operators. Those dynamical systems are infinite dimensional linear discrete dynamical systems and by using a matrix representation on the system we compute the iterates of such operators which are given by the powers of such matrices. Those matrices are sparse lower triangular matrices where only two subdiagonals are different than zero. The entries of the power matrices are calculated explicitly and with the aid of some particular cases we can show their contained dynamical information.