一類差分方程的全局吸引性與漸近穩(wěn)定性.pdf

1、華東師范大學(xué)代碼：102692u06屆碩士研究生學(xué)位論文一類差分方程的全局吸引性與漸近穩(wěn)定性院系專業(yè)研究方向?qū)熜彰T士研究生理工學(xué)院數(shù)學(xué)系應(yīng)用數(shù)學(xué)常微分方程朱德明教授李志二零零六年二月AbstractDi腦enceequationisasortofpower缸lmeanstoiIlvestigatetheruleoftIlediscretenaturalphenomeⅡaInrecent10years，therefore，thequm

2、itativea皿alysisofdifkrenceequationhasalwaysbeenthehotspotsubjects“【diedbytheresearcher8homeandabroadEspecially，anincreasinglymorenumberofresult8onrationaldifferenceequation，inViewthatwhichh8sasimplerform，arepllblishedInt

3、llisdissertation，weiⅡtroduceanewmethodwhichi8called“sllbsequencean以ysis”，toinvestigacetheglobalasymptoticalstabilityofakind《rationaldifferenceequ8tions硒thh遮horderAtflrst，westudyageneraldiffjrenceeauation：zn=，(a‰一l，zn～2，一

4、，z。一f)，n=1，2，3，(E)wherel≥1i8aninteger，，∈e((o，o。)2，(o，o。))，茹一卜1)∈(o，o。)f。rt=1，2，，fUndercert越nassumptioIls，weobtainasetof8umcientconditio璐forthedobalattractiveⅡessofequation(E)Then，whentheabovere8ultisapplied協(xié)thefoHowingdi

5、如renceequation：％∑m(z。一)z。9p(z。一p)t=1I≠巾lFon2—F——————————一∑皿(％一)。。一。蜘(z。一々)=I’≠wn=1，2，，(Elo)theglobalasymptoticalstabilityiSobtainedifsomecoIldition8aresatisBed，where七∈1，2)，m，p，g∈1，2，一，塒and勘，z一1，一，z一陸一1)arepositiverealiIl

6、itimv出ue8A8wecanseetha土thedi圩erenceequations8tudiedinthecitedreference8盯eau8pecialcase8ofequation(E10)Hence，ourre8ultincludesandextendsm舭l(fā)ycorrespondingresult8Moreover，itisconfirmedthattheideaof“subsequenceanaly8is”isqui