混沌講義1-混沌介紹

混沌控制與同伴及其在保密通信中的應(yīng)用：緒論

西南大學(xué)電子信息工程學(xué)院李傳東西南大學(xué)電子信息工程學(xué)院研究生課程2內(nèi)容蝴蝶效應(yīng)與混沌1混沌系統(tǒng)舉例2混沌同步概述3近幾年我們的工作45基于混沌滯同步的保密通信混沌滯同步63蝴蝶效應(yīng)與混沌蝴蝶效應(yīng)在南美洲亞馬遜河流域熱帶雨林中，一只蝴蝶漫不經(jīng)心地扇動(dòng)了幾下翅膀，可能在兩周后引起美國(guó)德克薩斯一場(chǎng)災(zāi)難性的風(fēng)暴。蝴蝶效應(yīng)舉例14蝴蝶效應(yīng)與混沌BenjaminFranklin.PoorRichard’sAlmanackin1758丟失一個(gè)釘子，壞了一只蹄鐵；

壞了一只蹄鐵，折了一匹戰(zhàn)馬；

折了一匹戰(zhàn)馬，傷了一位騎士；

傷了一位騎士，輸了一場(chǎng)戰(zhàn)斗；

輸了一場(chǎng)戰(zhàn)斗，亡了一個(gè)帝國(guó)。西方流傳的一首民謠蝴蝶效應(yīng)舉例25蝴蝶效應(yīng)《禮記·經(jīng)解》：“《易》曰：‘君子慎始，差若毫厘，繆以千里?！?/p>

機(jī)遇垂青有準(zhǔn)備的人蝴蝶效應(yīng)舉例36混沌現(xiàn)象簡(jiǎn)介蝴蝶效應(yīng)舉例4--"小蝴蝶"掀起美國(guó)政壇風(fēng)暴

小蝴蝶-萊溫斯基7混沌現(xiàn)象簡(jiǎn)介8蝴蝶效應(yīng)蝴蝶效應(yīng)舉例5－－"大蝴蝶"索洛斯刮起東亞金融風(fēng)暴9混沌現(xiàn)象簡(jiǎn)介蝴蝶效應(yīng)（ButterflyEffect）是指在一個(gè)動(dòng)力系統(tǒng)中，初始條件下微小的變化能引起整個(gè)系統(tǒng)長(zhǎng)期而巨大的連鎖反應(yīng)。這是一種混沌現(xiàn)象。此效應(yīng)說(shuō)明，事物發(fā)展的結(jié)果，對(duì)初始條件具有極為敏感的依賴性，初始條件的極小偏差，將會(huì)引起結(jié)果的極大差異。10哈肯：混沌性為來(lái)源于決定性方程的無(wú)規(guī)運(yùn)動(dòng)。費(fèi)根包姆：確定系統(tǒng)的內(nèi)在隨機(jī)運(yùn)動(dòng)。洛侖茲：確定性非周期流。赫柏林：沒(méi)有周期性的有序。錢(qián)學(xué)森：混沌是宏觀無(wú)序、微觀有序的現(xiàn)象。什么是混沌？11混沌現(xiàn)象簡(jiǎn)介確定性系統(tǒng)+確定性行為確定性系統(tǒng)+混沌行為產(chǎn)生混沌的內(nèi)在機(jī)制12混沌現(xiàn)象簡(jiǎn)介混沌是指確定的宏觀的非線性系統(tǒng)在一定條件下所呈現(xiàn)的不確定的或不可預(yù)測(cè)的隨機(jī)現(xiàn)象；是確定性與不確定性或規(guī)則性與非規(guī)則性或有序性與無(wú)序性融為一體的現(xiàn)象；其不可確定性或無(wú)序隨機(jī)性不是來(lái)源于外部干擾，而是來(lái)源于內(nèi)部的"非線性交叉耦合作用機(jī)制"，這種"非線性交叉耦合作用"的數(shù)學(xué)表式是動(dòng)力學(xué)方程中的非線性項(xiàng)，正是由于這種"交叉"作用，非線性系統(tǒng)在一定的臨界性條件下才表現(xiàn)出混沌現(xiàn)象，才導(dǎo)致其對(duì)初值的敏感性，才導(dǎo)致內(nèi)在的不穩(wěn)定性的綜合效果。產(chǎn)生混沌的內(nèi)在機(jī)制13混沌系統(tǒng)舉例。。。洛侖茲系統(tǒng)

Chua電路

Chen系統(tǒng)。。。

Ikeda系統(tǒng)

M-G系統(tǒng)

Liao神經(jīng)系統(tǒng)常用連續(xù)時(shí)間混沌系統(tǒng)常微分混沌系統(tǒng)時(shí)滯微分混沌系統(tǒng)14混沌系統(tǒng)舉例Lorenzsystem(Lorenz,1960s)Wherea,bandcareparameters15混沌系統(tǒng)舉例ChuaCircuit(Chua,)16混沌系統(tǒng)舉例Chenattractor(Chen)17混沌系統(tǒng)舉例RosslersystemRosslerattractor18混沌系統(tǒng)舉例M-GEquation19混沌系統(tǒng)舉例IkedaEquation20混沌系統(tǒng)舉例Liaomodel(Liao,2001)where混沌相關(guān)的期刊Chaos:AnInterdisciplinaryJournalofNonlinearScience

[1]Impulsivesynchronizationofchaoticsystems。ChuandongLi,XiaofengLiaoandXingyouZhang.Chaos15,023104(2005);[2]Synchronizationofaclassofcoupledchaoticdelayedsystemswithparametermismatch.TingwenHuang,ChuandongLiandXiaofengLiao.Chaos17,033121(2007);/10.1063/1.2776668[3]Switchcontrolforpiecewiseaffinechaoticsystems.ChuandongLi,XiaofengLiaoandXiaofanYang.Chaos16,033104(2006);/10.1063/1.2213676[3]Exponentialstabilizationofchaoticsystemswithdelaybyperiodicallyintermittentcontrol.ChuandongLi,XiaofengLiaoandTingwenHuang.Chaos17,013103(2007);/10.1063/1.2430394[4]Synchronizationofchaoticsystemswithdelayusingintermittentlinearstatefeedback.TingwenHuang,ChuandongLiandXinzhiLiu.Chaos18,033122(2008);/10.1063/1.2967848[5]Anticipatingsynchronizationofaclassofchaoticsystems.QiHan,ChuandongLiandTingwenHuang.Chaos19,023105(2009);/10.1063/1.3125755[6]Stabilityofpiecewiseaffinesystemswithapplicationtochaosstabilization.ChuandongLi,GuanrongChenandXiaofengLiao.Chaos17,023123(2007);/10.1063/1.2734905[7]Anticipatingsynchronizationofchaoticsystemswithtimedelayandparametermismatch.QiHan,ChuandongLiandJunjianHuang.Chaos19,013104(2009);/10.1063/1.3013600[8]Predictingchaosinmemristiveoscillatorviaharmonicbalancemethod.XinWang,ChuandongLi,TingwenHuangandShukaiDuan.Chaos22,043119(2012);/10.1063/1.4766675[9]Impulsivestabilizationandsynchronizationofaclassofchaoticdelaysystems.ChuandongLi,XiaofengLiao,XiaofanYangandTingwenHuang.Chaos15,043103(2005);/10.1063/1.2102107[10]Chaosquasisynchronizationinducedbyimpulseswithparametermismatches.ChuandongLi,GuanrongChen,XiaofengLiaoandZhengpingFan.Chaos16,023102(2006);混沌相關(guān)的期刊InternationalJournalofBifurcationandChaosThescope

experimental,computational,and

theoreticalaspectsof

bifurcations,chaos

and

complexity,aswellasclosely-relatednonlineardynamics,fractals,cellularandnonlineardynamicalnetworksofbiological,economic,engineering,fluiddynamic,neural,physical,social,andothercomplexsystems.

混沌相關(guān)的期刊BIFURCATIONANALYSISOFADISCRETE-TIMEKALDORMODELOFBUSINESSCYCLEXINGHE,CHUANDONGLI,YONGLUSHUInternationalJournalofBifurcationandChaosVol.22,No.081250186EXISTENCEANDGLOBALEXPONENTIALSTABILITYOFPERIODICSOLUTIONOFCELLULARNEURALNETWORKSWITHIMPULSESANDLEAKAGEDELAYHUIWANG,CHUANDONGLI,HONGBINGXUInternationalJournalofBifurcationandChaosVol.19,No.03,pp.831-842

ANTI-SYNCHRONIZATIONOFACLASSOFCOUPLEDCHAOTICSYSTEMSVIALINEARFEEDBACKCONTROLCHUANDONGLI,XIAOFENGLIAOInternationalJournalofBifurcationandChaosVol.16,No.04,pp.1041-1047

DELAY-DEPENDENTANDDELAY-INDEPENDENTSTABILITYCRITERIAFORCELLULARNEURALNETWORKSWITHDELAYSCHUANDONGLI,XIAOFENGLIAO,KWOK-WOWONGInternationalJournalofBifurcationandChaosVol.16,No.11,pp.3323-3340混沌研究牛人篇Guanrong

(Ron)Chen

ChairProfessor

IEEE

FellowDepartmentofElectronicEngineering

CityUniversityofHongKong

83TatCheeAvenue,Kowloon

HongKongSAR,P.R.China

(Phone)852-3442-7922

(Fax)

852-3442-0562

(Email)

gchen[at].hkDirector:

CentreforChaosandComplexNetworks混沌研究牛人篇1948年出生于廣州.因文革下鄉(xiāng)10年而沒(méi)有上過(guò)大學(xué)，通過(guò)插隊(duì)期間長(zhǎng)期自學(xué)，在文革結(jié)束時(shí)直接考入中山大學(xué)數(shù)學(xué)系第一屆研究生班，1981年秋畢業(yè)并獲計(jì)算數(shù)學(xué)碩士學(xué)位.隨后出國(guó)留學(xué)，于1987年春獲美國(guó)TexasA&M大學(xué)應(yīng)用數(shù)學(xué)博士學(xué)位.1987-1990年任美國(guó)Rice大學(xué)訪問(wèn)助理教授；1990-2000年先后任美國(guó)Houston大學(xué)助理教授、副教授、正教授；2000年至今任香港城市大學(xué)電子工程系講座教授及該?；煦缗c復(fù)雜網(wǎng)絡(luò)學(xué)術(shù)研究中心主任；2005-2009年任北京大學(xué)工學(xué)院的教育部“長(zhǎng)江學(xué)者”計(jì)劃講座教授.混沌研究牛人篇陳關(guān)榮教授的研究領(lǐng)域主要集中在工程科學(xué)的一個(gè)核心領(lǐng)域—非線性系統(tǒng)的動(dòng)力學(xué)分析和控制及其在復(fù)雜網(wǎng)絡(luò)和非線性科學(xué)等相關(guān)領(lǐng)域中的應(yīng)用.自1981年以來(lái),共發(fā)表了500余篇SCI雜志論文和近300篇國(guó)際會(huì)議論文，SCI他引20,000多次，單篇SCI最高他引1000多次，有20多篇論文單篇SCI引用超過(guò)100次，SCIh指數(shù)為77，被ISI評(píng)定為工程學(xué)以及物理學(xué)的高引用率研究人員.共出版25部研究專(zhuān)著、高等教材和編著，

混沌研究牛人篇LeonO.ChuaDistinguishedProfessor,TechnicalUniversityofMunich,GermanyProfessorEmeritus,UniversityofCaliforniaatBerkeley,USAElectedForeignMemberoftheEuropeanAcademyofSciences(AcademiaEuropaea)1997混沌研究牛人篇AwardsandPrizes:TheIEEEBrowderJ.ThompsonMemorialPrizeAward(1967)TheIEEEGuillemin-CauerAward(1972,1985,1989)TheIEEEW.R.G.BakerPrizePaperAward(1973)TheFrederickEmmonsAward(1974)TheAlexandervonHumboldtSeniorUSScientistAward(1982)TheIEEECentennialMedal(1985)TheIEEENeuralNetworksPioneerAward(2000)TheIEEEThirdMilleniumMedal(2000)TheIEEECircuitsandSystemsSocietyGoldenJubileeMedal(2000)混沌研究牛人篇TheIEEEGustavRobertKirchhoffAward(2005)TheMacE.VanValkenburgAward(1995and1998)TheIEEECircuitsandSystemsSocietyVitoldBelevitchAward(2007)TheGuggenheimFellowship(2010)LeverhulmeVisitingProfessor,UK(2010-2011)DistinguishedAffiliatedProfessor,TechnischeUniversitatMuenchen,Germany(2011-)混沌研究牛人篇Academician:AmericanNationalAcademyofSciences

AmericanAcademyofArtsandSciencesForeignMember:BrazilianAcademyofScienceFieldsMedalist:InternationalMathematicalUnionNationalScienceMedalist:USAWolfPrize:InternationalMathematicalUnionStevenSmaleUniversityProfessor,CityUniversityofHongKong混沌研究牛人篇GuanXinpingGuanZhihongHongYiguangJiangGuopingLiChangpinLiChunguangLiShujunLvJinhu35混沌同步概述混沌有害？混沌有用？1998年亞洲金融危機(jī)和美國(guó)股市風(fēng)暴1998年太平洋上出現(xiàn)的“厄爾尼諾”現(xiàn)象電路中混沌現(xiàn)象化學(xué)反應(yīng)中的混沌現(xiàn)象激光混沌混沌化電機(jī)驅(qū)動(dòng)在工業(yè)攪拌、壓實(shí)中的應(yīng)用混沌密碼學(xué)混沌保密通信36混沌同步概述

PecoraandCarroll,–-PCscheme.ViaconditionalLyapunovexponents,LorenzandRosslersystemsMuradiandLakshmanan,----unidirectionallycoupledchaoticsystemsCelka,-----delayedfeedbackapproachOsipov,-----bidirectionallycoupledsystemsTaoYang,----impulsivesynchronizationviaapulse37混沌同步概述Completesynchronization（完全同步）Generalizedsynchronization（廣義同步）Phasesynchronization（相同步）Lagsynchronization（滯同步）Anticipatesynchronization（前向同步）hybridsynchronization（混合同步）38混沌滯同步我們的工作LagsynchronizationDelayedlinearfeedbackapproachNonlinearobserverapproachImpulsivecontrolmethodsRobustlagsynchronizationforthechaoticsystemswithuncertaintyApplicationtosecurecommunication39混沌滯同步

完全同步是實(shí)際不可行的.

信號(hào)傳輸、電路開(kāi)關(guān)會(huì)使同步產(chǎn)生延遲.混沌滯同步的研究背景40混沌滯同步Problemformulation:whereNow,wewillderivetheconditionstobesatisfiedbycontrolitemsuchthat41混沌滯同步LettheerrorSo,theissueonlagsynchronizationcanbeshiftedintothatofthestabilityforerrorsystematThentheerrorcanbedescribedby42混沌滯同步Definition1.Ifthereexistk>0andr(k)>0suchthatRemark:Toguaranteethespeedofsynchronization,weshouldderivethecriteriaforexponentialstability.thenerrorsystemissaidtobeexponentiallystable,wherekiscalledthedegreeofexponentialstability.43混沌滯同步Here,weconsiderthefollowingerrorsystem:Theorem1.Supposethatthereexistthreepositivenumbersp,qandksuchthatthentheerrorsystemaboveisexponentiallystable.Moreover,44混沌滯同步Corollary1.1.Supposethatthereexistsapositivenumberk

suchthatthentheerrorsystemaboveisexponentiallystable.45混沌滯同步數(shù)值例子where46混沌滯同步LetFromTheorem1,wecanobtain,wherekisapositivenumber,calledthedegreeofexponentialstability.Thenerrorsystemisexponentiallystableat.Thus,thecoupledLiao’ssystemswithchaosareexponentiallysynchronizedTheorem2.Supposethatthereexistsascalark>0suchthat47混沌滯同步Fromtheorem2,wecancalculateorestimatethecontrolgainK.Here,weobtainSo,K*=9.0276whenk=0.1and

=1,whichimpliesfromTheorem2thatifK>K*,coupledLiao’ssystemsexponentiallysynchronize.48保密通信m(t)---informationsignalcontainingamessages(t)---transmittedchaoticsignal49保密通信

信號(hào)隱藏

信號(hào)調(diào)制

信號(hào)隱藏、調(diào)制m(t)---要發(fā)送的信息s(t)---實(shí)際的傳輸信號(hào)50保密通信Figure.AsimplifiedframeofChaoticsecurecommunication51立項(xiàng)背景基于混沌同步的保密通信系統(tǒng)混沌系統(tǒng)1混沌系統(tǒng)252保密通信基于滯同步的混沌保密通信EncryptionFunctionChaoticSystemPublicChannelDecryptionFunctionChaoticSystemDelaysg

m(t)

z(t)53保密通信Encryptiontransformation（加密變換）:Decryptiontransformation（解密變換）:where密碼算法54保密通信Operationintransmitter:ProducingkeystreamK(t)bychaoticsystemEncryptingmessagesignalm(t)bymeansofkeyK(t)Producingtransmittedsignalz(t)55保密通信Operationinreceiver:Receivingtransmittedsignalz(t)anddrivingchaoticsystemReconstructingencryptedsignalcen(t)ProducingkeystreamK(t)Decryptingcen(t)bymeansofkeyK(t)andthenretrievingm(t)56保密通信Actualtransmittedsignal:Transmitter:Receiver:數(shù)值例子57保密通信WeselectMCKcircuitasthechaoticsysteminthetransmitter,andletK(t)=x4(t).Taking=1,m(t)=sin(t)+1.5,,k=[-13.987,-0.1846,4.195,11.051],lagsynchronizationisachieved.Notethattheencryptedsignalrecoveredbythereceiveris58保密通信Therecoveredkey:Retrievedmessagesignal:Fromcontrollawobtainedabove,itfollows59保密通信Figure.Maskingandrecoveryofmessage.a)Actualtransmittedsignalwithtimeinterval[0,30].b)Therecoveredmessagesignalwithtimeinterval[0,29].60近幾年的主要工作驗(yàn)證、應(yīng)用和改進(jìn)建立新的分析工具提出新的控制理論框架混沌系統(tǒng)的非連續(xù)控制和同步61近幾年的主要