DYNAMICS AND GLOBAL BEHAVIOR FOR A FOURTH-ORDER RATIONAL DIFFERENCE EQUATION

Authors : E. M. ELSAYED, M. M. EL-DESSOKY

Pages : 479-494

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Publication Date : 2013-05-01

Article Type : Research Paper

Abstract :In this paper we study the behavior of the rational difference equationof the fourth orderx n+1 = ax n + bx n x n−2 cx n−2 + dx n−3 , n = 0, 1, ...,where the initial conditions x−3 , x −2 , x −1 , x are arbitrary positive realnumbers and a, b, c, d are positive constants. Also, we give the solutionof some special cases of this equation.
Keywords : difference equations, stability, boundedness, periodicity, solution of differ