Global asymptotic stability of a higher order rational difference equation
- Sun, Taixiang
- Xi, Hongjian
DOIAbstract
AbstractIn this note, we consider the following rational difference equation:xn+1=f(xn−r1,…,xn−rk)g(xn−m1,…,xn−ml)+1f(xn−r1,…,xn−rk)+g(xn−m1,…,xn−ml),n=0,1,…, where f∈C((0,+∞)k,(0,+∞)) and g∈C((0,+∞)l,(0,+∞)) with k,l∈{1,2,…}, 0⩽r1<⋯<rk and 0⩽m1<⋯<ml, and the initial values are positive real numbers. We give sufficient conditions under which the unique equilibrium x¯=1 of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the recent literature
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