Open AccessOn the oscillation of a third order rational difference equation
Author(s) -
R. Abo-Zeid
Publication year - 2015
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2014.03.001
Subject(s) - mathematics , oscillation (cell signaling) , character (mathematics) , order (exchange) , stability (learning theory) , third order , real number , matrix difference equation , pure mathematics , mathematical analysis , differential equation , riccati equation , philosophy , genetics , geometry , theology , finance , machine learning , computer science , economics , biology
In this paper, we discuss the global asymptotic stability of all solutions of the difference equationxn+1=Axn-2B+Cxnxn-1xn-2,n=0,1,…where A,B,C are positive real numbers and the initial conditions x-2,x-1,x0 are real numbers. Although we have an explicit formula for the solutions of that equation, the oscillation character is worth to be discussed