The behaviour of the positive solutions of the difference equation xn 5 A 1 xn 2 2 xn 2 1 p

Abstract

xn 1⁄4 Aþ xn22 xn21 p ; n 1⁄4 0; 1; . . .; with p, A [ (0, 1), p – 1 and x22, x21 [ (0, 1). It is shown that: (a) all solutions converge to the unique equilibrium, x 1⁄4 Aþ 1, whenever p # min{1, (A þ 1)/2}; (b) all solutions converge to period two solutions whenever (A þ 1)/2 , p , 1; and (c) there exist unbounded solutions whenever p . 1. These results… (More)

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