Analysis and qualitative behaviour of a tenth-order rational difference equation

Abstract

In this article, we examine the qualitative behavior of the solutions of the following di¤erence equation zn+1 = aZn-4 +bZn-4/cZn-4-dzn4; n = 0,1,.... where the initial conditions Z_9; Z_8; Z_7; Z_6; Z_5; Z_4; Z_3; Z_2; Z_1;Z0 are arbitrary non-zero real numbers and a, b, c, d are positive constants.