Asymptotic Analysis of a Two-Species Higher Order Rational Difference Model with Cross-Species Dependence

In this study, we analyze the asymptotic stability, persistence, and bounded behavior of the solutions to a system of higher-order rational difference equations. The model consists of two species, where the population of the first species in the n-th and (n − k)-th generations, along with the population of the second species in the n-th and (n − 1)-th generations, influences the growth of the first species. Similarly, the growth of the second species is determined by the population of the second species in the n-th and (n − k)-th generations, along with the population of the first species in the n-th and (n − 1)-th generations.