Global attractivity in nonlinear difference equations of higher order with a forcing term

D.D. Hai and C. Qian

Applied Mathematics and Computation, 2015, vol. 264, issue C, 198-207

Abstract: Consider the following nonlinear difference equation of order k + 1 with a forcing term (0.1)xn+1−anxn+bnf(xn−k)=rn,n=0,1,…where {an} is a positive sequence in (0, 1], {bn} is a positive sequence, {rn} is a real sequence, k is a nonnegative integer, and f: (τ, ∞) → (τ, ∞) is a continuous function with −∞ ≤ τ ≤ 0. We establish a sufficient condition for every solution of Eq. (0.1) to converge to zero as n → ∞. Several new global attractivity results are obtained for some special cases of Eq. (0.1) which have been studied widely in the literature. Our results can be applied to some difference equations derived from mathematical biology.

Keywords: Nonlinear difference equations of higher order; Forcing term; Global attractivity; Biological models (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:198-207

DOI: 10.1016/j.amc.2015.04.086

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