Table Of ContentNonlinear 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
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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
