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We consider the following nonlinear difference equation:xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} andk,t∈{1,2,…} with 0≤m<t(k+1)−1, the initialvalues x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞),and {pn}n=0∞ is a positive sequence of the periodk+1. We give sufficient conditions under which every positivesolution of this equation tends to the period k+1 solution

discrete dynamics in nature and society

On the global behavior of the nonlinear difference equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E1"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:…

On the global behavior of the nonlinear difference equationxn+1=f(pn,xn−m