Local attractivity and periodic character of rational Difference equation

Abstract

In this thesis, we investigate some behaviors of the rational difference equations [symbol] where k ∈ℕ, the parameters A,B0,B1,B2, . . . ,Bk, and the initial conditions x−k, x−k+1, x−k+2, . . . ,x0 are nonnegative real numbers. We classify all periodic solutions with prime period-two and prime period-three. Then, we also present the existence of periodic solutions with prime period-p, where p is a prime number. Moreover, we prove the convergence of solutions to a period-(k + 1) solution. Finally, the local attractivity of solutions about some periodic with prime periodtwo and prime period-three is established.