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Nonlinear Systems and Complexity Series Editor: Albert C. J. Luo Valentin Afraimovich José António Tenreiro Machado Jiazhong Zhang Editors Complex Motions and Chaos in Nonlinear Systems Nonlinear Systems and Complexity SeriesEditor AlbertC.J.Luo SouthernIllinoisUniversity Edwardsville,IL,USA Moreinformationaboutthisseriesathttp://www.springer.com/series/11433 Valentin Afraimovich José António Tenreiro Machado (cid:129) Jiazhong Zhang Editors Complex Motions and Chaos in Nonlinear Systems 123 Editors ValentinAfraimovich JoséAntónioTenreiroMachado SanLuisPotosiUniversity InstituteofEngineering SanLuisPotosi,Mexico PolytechnicofPorto Porto,Portugal JiazhongZhang SchoolofEnergyandPowerEngineering Xi’anJiaotongUniversity ShaanxiProvince,China ISSN2195-9994 ISSN2196-0003 (electronic) NonlinearSystemsandComplexity ISBN978-3-319-28762-1 ISBN978-3-319-28764-5 (eBook) DOI10.1007/978-3-319-28764-5 LibraryofCongressControlNumber:2016931338 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland Preface Tenchaptersarecollectedinthiseditedbook,andtheyarerelatedtomathematical modeling, numerical methods, and applications in nonlinear dynamics to provide a deep understanding of complex phenomena in nonlinear systems. In particular, somechaptersfocusonnonlinearphenomena,numericalmethods,andLagrangian coherent structures in fluid dynamics, which are governed by nonlinear partial differential equations. The chapters of this edited book were taken from the 5th International Conference on Nonlinear Science and Complexity, held in Xi’an, China, in 2014 (NSC 2014). The aim of this conference was to present the fundamental and cutting-edge theories and techniques for modern science and technologyand to stimulate moreresearch interest in the explorationof nonlinear science and complexity. The conference focuses on fundamental theories and principles, analytical and symbolic approaches, and computational techniques in nonlinearphysicalscience and nonlinearmathematics. The chaptersof this edited book are based on invited lectures, with extended results in nonlinear dynamical systems.Thechapterscoverthefollowingtopics: (cid:129) Detectionofquasi-periodicprocessesinexperimentalmeasurements (cid:129) Input–outputmechanismofdiscretechaosextensionanditsapplications (cid:129) HiddendimensionsinaHamiltoniansystemonnetworks (cid:129) Discontinuousdynamicalsystemsandsynchronization (cid:129) Steady-statesolutionforaRayleighpistoninatemperaturegradient (cid:129) Analyticalperiodicsolutionsinnonlineardynamicalsystems (cid:129) Singularitiesinfluiddynamicsandtheirnumericalmethods (cid:129) Lagrangiandynamcsinfluidmechanicsandnumericalmethods (cid:129) Nonlineardynamicsinplasmaflowandflowcontrols (cid:129) Numericalmethodsforfluid–structureinteractionsandlock-inbehaviors Manypaperspresentedgivenattheconferencepresentedexcellentachievements in nonlinearscience and complexity.At the conference,some comprehensivedis- cussions,ledbytheinvitedrecognizedscientists,wereheldontheaforementioned topics.Fromsuchdiscussionstheyoungscientistandstudentattendeeslearnednew methods,ideas,andresultsandbenefitedfromtheirattendanceattheconference. v vi Preface The editors would like to acknowledge the financial support of the National ScienceFoundationofChinaandXi’anJiaotongUniversityandthanktheauthors andreviewersfortheirsupportofthe conferenceandthe collectionofpapers.We hopetheresultspresentedinthisbookwillbeusefulforotherspecialistsinscience andengineeringrelatedtocomplexdynamicalsystems. SanLuisPotosi,Mexico ValentinAfraimovich Porto,Portugal JoséAntónioTenreiroMachado ShaanxiProvince,China JiazhongZhang Contents 1 DetectionofQuasi-PeriodicProcessesinExperimental Measurements:Reductiontoan“IdealExperiment”.................. 1 R.R.Nigmatullin 2 Some Singularities in Fluid Dynamics and Their BifurcationAnalysis........................................................ 39 JiazhongZhangandYanLiu 3 Finite-ElementAnalysisofNonlinearFluid–Membrane InteractionsUsingaModifiedCharacteristic-BasedSplit (CBS)Scheme............................................................... 75 XuSunandJiazhongZhang 4 Lock-InBehaviorsofanAirfoilwithLocalExcitation inLow-Reynolds-NumberFlow........................................... 107 WeiKangandXiangyanDai 5 NanosecondPulsedPlasmaFlowControl:ProgressandProblems... 137 YunWu,MinJia,HuaLiang,HuiminSong,andYinghongLi 6 HiddenDimensionsinanHamiltonianSystemonNetworks.......... 173 SarahdeNigrisandXavierLeoncini 7 Input–OutputMechanismoftheDiscrete ChaosExtension............................................................ 203 MaratAkhmetandMehmetOnurFen 8 Steady State Solution for a Rayleigh’s Piston inaTemperatureGradient................................................ 235 SimonVillain-Guillot vii viii Contents 9 AnalyticalPeriod-mMotionsinaParametric,Quadratic NonlinearOscillator........................................................ 247 AlbertC.J.LuoandBoYu 10 Periodic Motions to Chaos in Duffing Oscillator via DiscretizationTechnique................................................... 259 YuGuoandAlbertC.J.Luo Chapter 1 Detection of Quasi-Periodic Processes in Experimental Measurements: Reduction to an “Ideal Experiment” R.R.Nigmatullin Abstract In this chapter, a general concept for the consideration of any reproducible data, measured in many experiments, in one unified scheme is proposed. In addition, it has been demonstrated that successive and reproducible measurementshave a memory, and this important fact makes it possible to group alldataintotwolargeclasses:idealexperimentswithoutmemoryandexperiments with memory. Real data with memory can be defined as a quasi-periodic process andareexpressedintermsofthePronydecomposition(thispresentationservesas the fitting functionfor the quantitativedescriptionof the data), while experiments withoutmemoryareneededtopresentafragmentoftheFourierseriesonly.Inother words,a measuredfunctionextractedfromreproducibledatacan havea universal quantitativedescriptionexpressedintheformoftheamplitude-frequencyresponse (AFR)thatbelongstothegeneralizedPronyspectrum(GPS).Theproposedscheme is rather general and can be used to describe all kinds of experiments that can be reproduced (with acceptable accuracy) within a certain period of time. The proposedgeneralalgorithm makes it possible to consider many experimentsfrom a unified point of view. Two real examples taken from physics (X-ray scattering measurements) and electrochemistry confirm this general concept. A unified so- called bridge between the treated experimental data and a set of competitive hypothesesthatare supposedtodescribedthemisdiscussed.The generalsolution oftheproblem,wheretheapparatusfunctioncanbeaccuratelyeliminatedandthe measured data can be reduced to an “ideal” experiment, is presented. The results obtainedin this paper help to formulatea new paradigmin data/signalprocessing forawideclassofcomplexsystems(especiallyincaseswherethebestfitmodelis absent),andtheconventionalconceptionassociatedwiththetreatmentofdifferent measurements should, from our point of view, be reconsidered. As an alternative approach we considered also the nonorthogonal amplitude-frequency analysis of R.R.Nigmatullin((cid:2)) RadioelectronicandInformative-MeasurementsTechnicsDepartment,KazanNationalResearch TechnicalUniversity,10KarlMarxSt.,420011Kazan,Tatarstan,Russia e-mail:[email protected] ©SpringerInternationalPublishingSwitzerland2016 1 V.Afraimovichetal.(eds.),ComplexMotionsandChaosinNonlinearSystems, NonlinearSystemsandComplexity15,DOI10.1007/978-3-319-28764-5_1