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ID:34600519
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页数:34页
时间:2019-03-08
《一类分片线性系统动力学性质地研究》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、一类分片线性系统的动力学性质研究摘要本文主要研究了一类分四片的平面线性分片系统的动力学行为.随着科技的发展,物理,化学等领域的许多模型需要分片光滑系统来描述.因此,对这类系统的研究具有重要的理论意义和应用价值.与光滑系统相比,分片光滑系统更为复杂,尤其是扰动后的分片光滑系统,主要体现在不光滑处.本文考虑的这类系统还具有对称性,具体形式如下:IF+(z,Ⅳ),z>o,暑,>o,(主)=Fcz,∥,={:二{三:;;:三三:::三三:ct,IF+(z,y),z2、,我们只需要考虑第一,四象限的轨线情况,即可判别整个系统的动力学性态.首先,我们利用P0.mcar∈映射P'得到了系统(1)的一些性质,如平衡点的类型和稳定性,还证明了未扰系统不存在极限环.进而,我们研宄系统(1)的0阶对称扰动系统,再构造PoiIlc缸占映射户,分析了九种类型的分支情况.并且,证明了至多存在一个仅包围原点的极限环,至多存在一个包围所有奇点(包括广义奇点)或分界点的极限环.事实上,本文给出的结论同样在非对称系统及非对称扰动中成立.关键词:分片线性系统,扰动,回归映射,平衡点,分支,极限环THEQUALITATIVEANAL.YSISoFACLASSOFPIECEW3、ISELINEARSYSTEMABSTRACTThiSp印erde色k丽ththedyll删cbeha舫0r0facla蹈0fpL衄arpiece丽鼬hear踟te脚而thfolIrzon皓.Withthedevelopment0fscience觚dtechnol-9酗ma珂mod出inthe丘eIdsofphysi∞,che谳巧如d∞∞a舱de∞ribedbypieceⅣislesm00th对stem.Theref6re,thestudyOfsuch眄stemisofimportanttheo陀tic8lsigni丘canceandpraucticalV址ue.Compared4、withsmooth科st朗鸲,piec印婚眙sm00thsysteInsaremo陀ca忸pI∞【’箦peciauytheperturbeds辨;tems,whicha弛mainlyenlbodiedinn∞-sm00thbo皿d8匝y.Mor∞『、,er,the舛eminthi8paperissyn姗etric,ofwhichtheconcretefomi8粥foUOW8:IF+(z,矽),z>o,y>o,(;)=Fcz,暑,,={;二{二:;;:三三三:蚤妻三:cl,IP+(z,Ⅳ),z5、ngtoits母皿衄etricch缸们ter,itisonlyn∞楣sa珂toc戚derthetrajeC.tori∞inthe触a丑dthefourthquadr劬1t,andthenthed:)m锄icbeh8访orcOuldbeidenti丘edLFi瑙tly’by憾ingP0incar6m印尸,∞mel。eypropert涵ofsystem(1)a舱provided,i11clumngstabili锣姐d霹∞metricalproperti豁ofeqIIilibriumpoints,曲ditisprovedthe陀isn0anyUmitcycleinunpertlIrbe6、d固咸em.沁∞dly'矾i删髑tigatetheperturbedsystemofsystem(1)丽thperturbeditemswhichi80forder0,stnlcturingPoinc缸占mapP,an啦胁gthebimrcati∞0fninetyp铭.FIurthemo弛,iti8provedth8tthe他i8a七m06t∞elilnit仍,cle8ur.roun出ngtheuniq■e8in91ll缸point,namel弧theorigin,andthe他i8atm06toneliImtcyclesu力.0un如gansin“larpoints(iIlcl7、udinggeneraHzedsingularpoints)andsep鲫atri)【points.Infl配t,thecl曲璐inthispapercanals0besh帆miIlthec躐0fnon-咖metric瓣e磁锄dnon.舄瑚1etricperturbations.KEYWoRDS:PieCewiseHnearsyste脚,perturb,Poinc喇m印,eq讪bri吼pOints,bi缸rcation,liIllitCycle第一章绪论1.1预备知识及相关背景l
2、,我们只需要考虑第一,四象限的轨线情况,即可判别整个系统的动力学性态.首先,我们利用P0.mcar∈映射P'得到了系统(1)的一些性质,如平衡点的类型和稳定性,还证明了未扰系统不存在极限环.进而,我们研宄系统(1)的0阶对称扰动系统,再构造PoiIlc缸占映射户,分析了九种类型的分支情况.并且,证明了至多存在一个仅包围原点的极限环,至多存在一个包围所有奇点(包括广义奇点)或分界点的极限环.事实上,本文给出的结论同样在非对称系统及非对称扰动中成立.关键词:分片线性系统,扰动,回归映射,平衡点,分支,极限环THEQUALITATIVEANAL.YSISoFACLASSOFPIECEW
3、ISELINEARSYSTEMABSTRACTThiSp印erde色k丽ththedyll删cbeha舫0r0facla蹈0fpL衄arpiece丽鼬hear踟te脚而thfolIrzon皓.Withthedevelopment0fscience觚dtechnol-9酗ma珂mod出inthe丘eIdsofphysi∞,che谳巧如d∞∞a舱de∞ribedbypieceⅣislesm00th对stem.Theref6re,thestudyOfsuch眄stemisofimportanttheo陀tic8lsigni丘canceandpraucticalV址ue.Compared
4、withsmooth科st朗鸲,piec印婚眙sm00thsysteInsaremo陀ca忸pI∞【’箦peciauytheperturbeds辨;tems,whicha弛mainlyenlbodiedinn∞-sm00thbo皿d8匝y.Mor∞『、,er,the舛eminthi8paperissyn姗etric,ofwhichtheconcretefomi8粥foUOW8:IF+(z,矽),z>o,y>o,(;)=Fcz,暑,,={;二{二:;;:三三三:蚤妻三:cl,IP+(z,Ⅳ),z5、ngtoits母皿衄etricch缸们ter,itisonlyn∞楣sa珂toc戚derthetrajeC.tori∞inthe触a丑dthefourthquadr劬1t,andthenthed:)m锄icbeh8访orcOuldbeidenti丘edLFi瑙tly’by憾ingP0incar6m印尸,∞mel。eypropert涵ofsystem(1)a舱provided,i11clumngstabili锣姐d霹∞metricalproperti豁ofeqIIilibriumpoints,曲ditisprovedthe陀isn0anyUmitcycleinunpertlIrbe6、d固咸em.沁∞dly'矾i删髑tigatetheperturbedsystemofsystem(1)丽thperturbeditemswhichi80forder0,stnlcturingPoinc缸占mapP,an啦胁gthebimrcati∞0fninetyp铭.FIurthemo弛,iti8provedth8tthe他i8a七m06t∞elilnit仍,cle8ur.roun出ngtheuniq■e8in91ll缸point,namel弧theorigin,andthe他i8atm06toneliImtcyclesu力.0un如gansin“larpoints(iIlcl7、udinggeneraHzedsingularpoints)andsep鲫atri)【points.Infl配t,thecl曲璐inthispapercanals0besh帆miIlthec躐0fnon-咖metric瓣e磁锄dnon.舄瑚1etricperturbations.KEYWoRDS:PieCewiseHnearsyste脚,perturb,Poinc喇m印,eq讪bri吼pOints,bi缸rcation,liIllitCycle第一章绪论1.1预备知识及相关背景l
5、ngtoits母皿衄etricch缸们ter,itisonlyn∞楣sa珂toc戚derthetrajeC.tori∞inthe触a丑dthefourthquadr劬1t,andthenthed:)m锄icbeh8访orcOuldbeidenti丘edLFi瑙tly’by憾ingP0incar6m印尸,∞mel。eypropert涵ofsystem(1)a舱provided,i11clumngstabili锣姐d霹∞metricalproperti豁ofeqIIilibriumpoints,曲ditisprovedthe陀isn0anyUmitcycleinunpertlIrbe
6、d固咸em.沁∞dly'矾i删髑tigatetheperturbedsystemofsystem(1)丽thperturbeditemswhichi80forder0,stnlcturingPoinc缸占mapP,an啦胁gthebimrcati∞0fninetyp铭.FIurthemo弛,iti8provedth8tthe他i8a七m06t∞elilnit仍,cle8ur.roun出ngtheuniq■e8in91ll缸point,namel弧theorigin,andthe他i8atm06toneliImtcyclesu力.0un如gansin“larpoints(iIlcl
7、udinggeneraHzedsingularpoints)andsep鲫atri)【points.Infl配t,thecl曲璐inthispapercanals0besh帆miIlthec躐0fnon-咖metric瓣e磁锄dnon.舄瑚1etricperturbations.KEYWoRDS:PieCewiseHnearsyste脚,perturb,Poinc喇m印,eq讪bri吼pOints,bi缸rcation,liIllitCycle第一章绪论1.1预备知识及相关背景l
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