離散競爭動力系統(tǒng)的一般性質(zhì)及反應(yīng)擴(kuò)散方程解的收斂性.pdf

1、中國科學(xué)技術(shù)大學(xué)博士學(xué)位論文離散競爭動力系統(tǒng)的一般性質(zhì)及反應(yīng)擴(kuò)散方程解的收斂性姓名：王毅申請學(xué)位級別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：蔣繼發(fā)2002.4.1AbstractThisthesisconsistsoftwopartsInthefirstpart，forcompetitivediscrete—timedynamicalsystemsonastronglyorderedtopologicalvectorspaceweprovetha

2、tanyQ—oru—limitsetisunorderedandliesonsomeinvarianthypersurfacewithcodimensionone，whichgeneralizesMWHirsch’sresultsforcompetitiveautononloussystemsofor—dinarydifferentialequationstocompetitivemapsinaverygeneralframeworka

3、ndimpliestheSarkovskii’STheoremforplanarstronglycompetitivemapsWealsooffersomecriteriaforplanarcompetitivemapshavingchaosFurther—more，weapplythisabstractresulttostudytheasymptoticbehavioroftheKohnogorovtypecompetitivemap

4、ping，whichisthePoincar6mapofgeneraltime—periodicKohnogorovtypecompetitivesystemsdescribedbyODEs：idxFi=z。，l(￡，Tl，z2，，z。)，z?！輔，1≤i≤nMoreprecisely，undertheassumptionsofDissipation，CompetitionandStrongCompetition，weprovethat

5、thereisacanonicallydefinedcountablefamilyofunordered，disjointinvariantsetswhichattractallpersistenttrajectorieswhoseu—limitsetsarenotcyclesMoreover，undertheassumptionsthattheoriginisa卻e，。rand差o，wesn。w恤attnereisauniquecar

6、ryingsimplexEattractingallnontrivialorbits，whichgivesanaffirmativeanswertothe“SmithConjecture”andsolvesmanyotherrelatedopenproblems(cf[122】)Furthermore，thesmoothnessofEisalsostudiedUndertheassumptionsofpropersmoothnessan

7、dweakpersistenceofthesystem。weprovethat∑isC1inthesecondpart，wecreateanewmethodincomparingthelimitsetcv(u)withsomespecialfixedpoint(equilibrium)PandconstrufiLaninteger—valuedfunctionⅣ(“，p)Usingsuchafunction，wefirstproveth

8、econvergencetofixedpointforsubhomogeneousandmonotonediscrete—timedynamicalsystem，andthentheconvergencetosteadystateofquasimonotonereactiondiffusionsystems，whichareeithersubhomogeneous，orweakly—subhomogeneousorwithanfirst