Discrete Dynamics in Nature and Society (Jan 2012)
On the Dynamics of a Higher-Order Difference Equation
Abstract
This paper deals with the investigation of the following more general rational difference equation: π¦π+1=πΌπ¦πβ/(π½+πΎππ=0π¦ππβ(2π+1)βππ=0π¦πβ(2π+1)), π=0,1,2,β¦, where πΌ,π½,πΎ,πβ(0,β) with the initial conditions π₯0,π₯β1,β¦,π₯β2π,π₯β2πβ1β(0,β). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented.