全衛(wèi)貞,李曉培,黃日娣,王麗,周敬人,劉付瀅,江建偉,劉世祺
一類高階有理差分方程的動力學性質
全衛(wèi)貞1,2,李曉培1,2,黃日娣1,2,王麗1,2,周敬人1,2,劉付瀅1,2,江建偉1,2,劉世祺1,2
(1.湛江幼兒師范??茖W校 數學系,廣東 湛江 524037;2. 嶺南師范學院 基礎教育學院,廣東 湛江 524037)
差分方程;平衡解;局部漸近穩(wěn)定;全局漸近穩(wěn)定;素二周期解
受上述研究的啟發(fā),本文研究高階差分方程
考慮差分方程
顯然,方程(5)與方程(3)等價,方程(3)又與方程(1)等價.所以判斷方程(1)解的穩(wěn)定性態(tài)可以轉化為判斷方程(5)解的穩(wěn)定性態(tài).
分3種情形來證明:
定理4差分方程(1)無素二周期解.
圖1 差分方程解的圖像
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Dynamic properties of a class of higher order rational difference equations
QUAN Weizhen1,2,LI Xiaopei1,2,HUANG Ridi1,2,WANG Li1,2,ZHOU Jingren1,2,LIU Fuying1,2,JIANG Jianwei1,2,LIU Shiqi1,2
(1. Department of Mathematic,Zhanjiang Preschool Education College,Zhanjiang 524037,China; 2. School of Basic Education,Lingnan Normal University,Zhanjiang 524037,China)
difference equation;equilibrium solution;local asymptotic stability;global asymptotic stability;prime two periodic solutions
1007-9831(2023)07-0001-05
O175.7
A
10.3969/j.issn.1007-9831.2023.07.001
2022-10-01
國家自然科學基金項目(11761011);廣東省普通高校特色創(chuàng)新項目(2020KTSCX351)
全衛(wèi)貞(1980-),女,廣西玉林人,副教授,碩士,從事差分方程與動力系統(tǒng)研究.E-mail:quan801015@126.com