THE RULE OF TRAJECTORY STRUCTURE AND GLOBAL ASYMPTOTIC STABILITY FOR A FOURTH-ORDER RATIONAL DIFFERENCE EQUATION

- Journal title : Journal of the Korean Mathematical Society
- Volume 44, Issue 4, 2007, pp.787-797
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2007.44.4.787

Title & Authors

THE RULE OF TRAJECTORY STRUCTURE AND GLOBAL ASYMPTOTIC STABILITY FOR A FOURTH-ORDER RATIONAL DIFFERENCE EQUATION

Li, Xianyi; Agarwal, Ravi P.;

Li, Xianyi; Agarwal, Ravi P.;

Abstract

In this paper, the following fourth-order rational difference equation , n=0, 1, 2,..., where a, b [0, ) and the initial values , is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

Keywords

rational difference equation;semicycle;cycle length;global asymptotic stability;

Language

English

Cited by

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