Trajectory structure rule of a third-order nonlinear difference equation

Szczegóły
Opis

Tytuł:: Trajectory structure rule of a third-order nonlinear difference equation
Autorzy:: PAN Zhikang
LI Xianyi
Temat:: nonlinear difference equation
nontrivial solution
cycle length
oscillation and nonoscillation
global asymptotic stability
Science (General)
Q1-390
Źródło:: Journal of Shanghai Normal University (Natural Sciences), Vol 49, Iss 3, Pp 261-269 (2020)
Wydawca:: Academic Journals Center of Shanghai Normal University, 2020.
Rok publikacji:: 2020
Kolekcja:: LCC:Science (General)
Typ dokumentu:: article
Opis pliku:: electronic resource
Język:: English
Chinese
ISSN:: 1000-5137
Relacje:: http://shnu.ijournals.cn/zrkxb/shsfqkszrb/ch/reader/view_abstract.aspx?file_no=20200302; https://doaj.org/toc/1000-5137
DOI:: 10.3969/J.ISSN.1000-5137.2020.03.002
Dostęp URL:: https://doaj.org/article/37f154c0b8cc49c1b4f5bf346184590c Link otwiera się w nowym oknie
Numer akcesji:: edsdoj.37f154c0b8cc49c1b4f5bf346184590c
: Czasopismo naukowe

In this paper the dynamics for a third-order nonlinear difference equation is considered in detail. By utilizing some beautiful mathematical skills, we describe the rule for the trajectory structure of this equation clearly and completely. The successive lengths of positive and negative semicycles of any nontrivial solutions of this equation occur periodically with prime period 7; the rule is 3+, 2-, 1+, 1- in a period. Using the rule, we verify that the positive equilibrium point of the equation is globally asymptotically stable.

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