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The Rule of Trajectory Structure and Global Asymptotic Stability for a Fourth-Order Rational Difference Equation

Ravi P. Agarwal|Xianyi Li
대한수학회 (The Korean Mathematical Society)|2007.07|대한수학회지 (Journal of the KMS)|제44권 제4호|pp. 787-797

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Abstract

In this paper, the following fourth-order rational dierenceequationxn +1 =xbn + xn 2xbn 3 + axbn xn 2 + xbn 3 + a; n = 0 ;1;2;:;where a;b 2 [0;1 ) and the initial values x 3;x 2;x 1;x0 2 (0; 1 ),is considered and the rule of its trajectory structure is described clearlyout. Mainly, the lengths of positive and negative semicycles of its nontriv-ial solutions are found to occur periodically with prime period 15. Therule is 1+ ;1 ;1+ ;4 ;3+ ;1 ;2+ ;2 in a period, by which the positiveequilibrium point of the equation is veried to be globally asymptoticallystable.

참고문헌 (12)

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  5. "Rate of convergence of solutions of rational dif-ference quation of second order", (2), pp.121~139 (2004)
  6. "Global behavior of nonlinear dierence quations of higherorder with applications" (1993), Kluwer Academic Publishers
  7. "The Dynamics ofxn +1 =+ x nA + Bx n + Cx n 1: Facts and Conjectures", 45(6-9), pp.1087~1099 (2003)
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  12. "Positive nonlinear dierence quations: some results and applications", 47(7), pp.4707~4717 (2001)

관련 논문AI추천

Global asymptotic stability of a higher order difference equationAlaa E. Hamza, R. Khalaf-Allah대한수학회 · 대한수학회보2007 · 제44권 제3호Asymptotic Results for a Class of Fourth Order Quasilinear Difference EquationsEthiraju Thandapani, Rajamannar Dhanasekaran, Subbiah Pandian경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제4호The Dynamics and Global Attractivity of a Rational Difference EquationAbdul Khaliq, E. M. Elsayed장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제1호Behavior of Solutions of a Fourth Order Difference EquationRaafat Abo-Zeid경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Asymptotic Behavior of Solutions of a Class of Second Order Quasilinear Difference EquationsE. Thandapani, R. K. Balasubramanian, S. Pandian경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제2호Periodicity and stability of solutions of higher order rational difference equationE. M. Elsayed, R. P. Agarwal장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제17권 제2호

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