Qualitative Behavior of Rational Difference Equation of Big Order

Abstract

We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequencexn+1=axn-l+bxn-x/c+dxn-lxn-k,n=0,1,…,where the parametersa, b, c,anddare positive real numbers, and the initial conditionsx-t,x-t+1,…,x-1andx0are positive real numbers wheret=maxk,l.

Global Attractor of Solutions of a Rational System in the Plane

“…Let ≥ 0 and , > 0. Let be defined by (7) and let { } ∈N 0 be a positive solution of (6) such that 0 1 > . Assume that the subsequence { 2 } ∈N 0 converges to e > 0.…”

“…Rational systems of first-order difference equations in the plane have been receiving increasing attention in the last decade. Recently, in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] (see also the references therein), efforts have been made for a more systematic approach. In particular, the rational system…”

Global Dynamics of Rational Difference Equations xn+1=xn+xLiu1, Peng2, Wang3 2017Discrete Dynamics in Nature and Society2040View full textAdd to dashboardCite

“…Several global asymptotic results for some special cases of (3) were obtained in [3][4][5][6][7][8][9][10][11][12][13].…”