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Behavior of Solutions of a Fourth Order Difference Equation

Raafat Abo-Zeid
경북대학교 자연과학대학 수학과|2016.06|Kyungpook Mathematical Journal|제56권 제2호|pp. 507-516

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키워드

periodic solutionconvergence.difference equation
주제분류수학

초록

In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation$$x_{n+1}=\frac{ax_{n-3} }{b- cx_{n-1}x_{n-3}},\qquad n=0,1,\ldots $$where $a,b,c$ are positive real numbers and the initial conditions $x_{-3},x_{-2},x_{-1},x_0$ are real numbers.

Abstract

In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation$$x_{n+1}=\frac{ax_{n-3} }{b- cx_{n-1}x_{n-3}},\qquad n=0,1,\ldots $$where $a,b,c$ are positive real numbers and the initial conditions $x_{-3},x_{-2},x_{-1},x_0$ are real numbers.

참고문헌 (17)

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  9. E. A. Grove, "Periodicities in Nonlinear Difference Equations", pp.2005, Chapman and Hall
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관련 논문AI추천

On the Solution of Fourth-Order Rational Recursive SequenceE. M. Elsayed, R.P. Agarwal장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제4호The Dynamics and Global Attractivity of a Rational Difference EquationAbdul Khaliq, E. M. Elsayed장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제1호Dynamics of Recursive Sequence of Order TwoElsayed Mohammed Elsayed경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제4호Periodicity and stability of solutions of higher order rational difference equationE. M. Elsayed, R. P. Agarwal장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제17권 제2호The expressions of solutions and periodicity for some nonlinear systems of rational di¤erence equationsE. M. Elsayed장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제3호Dynamical Behavior of a Third-Order Difference Equation with Arbitrary PowersMehmet Gumus, Ozkan Ocalan, Raafat Abo-Zeid경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제2호

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