The suggested study’s main objective is to create a new meaning for the word “homogeneous system.” With m being a positive integer, this phrase describes a P-self-semi-homogenous system of difference equations on the order of magnitude m. Furthermore, we introduced theorems for scenarios where P equals one and those where it takes any number. Every situation has a value of m, of which some are greater than one and some are equal to one. We provide examples to support each of these values.