Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering

481 Pages·2013·24.45 MB·English

by  Krzysztof Czolczynski

Studies in Computational Intelligence 483
Kyandoghere Kyamakya
Wolfgang A. Halang
Wolfgang Mathis
Jean Chamberlain Chedjou
Zhong Li (Eds.)
Selected Topics
in Nonlinear Dynamics
and Theoretical Electrical
Engineering
1 3
Studies in Computational Intelligence 483
Editor-in-Chief
Prof.JanuszKacprzyk
SystemsResearchInstitute
PolishAcademyofSciences
ul.Newelska6
01-447Warsaw
Poland
E-mail:[email protected]
Forfurthervolumes:
http://www.springer.com/series/7092
Kyandoghere Kyamakya, Wolfgang A. Halang,
Wolfgang Mathis, Jean Chamberlain Chedjou,
and Zhong Li (Eds.)
Selected Topics
in Nonlinear Dynamics
and Theoretical Electrical
Engineering
ABC
Editors
Univ.-Prof.Dr.-Ing.KyandoghereKyamakya Ass.Prof.Dr.-Ing.JeanChamberlainChedjou
Alpen-AdriaUniversitätKlagenfurt Alpen-AdriaUniversitätKlagenfurt
Klagenfurt Klagenfurt
Österreich Österreich
Prof.Dr.Dr.WolfgangA.Halang apl.Prof.Dr.habil.ZhongLi
FernuniversitätHagen FernuniversitätHagen
Philipp-Reis-Gebäude Philipp-Reis-Gebäude
Hagen Hagen
Deutschland Deutschland
Prof.WolfgangMathis
InstitutfürTheoretischeElektrotechnik
LeibnizUniversitätHannover
Hannover
Deutschland
ISSN1860-949X ISSN1860-9503 (electronic)
ISBN978-3-642-37780-8 ISBN978-3-642-37781-5 (eBook)
DOI10.1007/978-3-642-37781-5
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013935709
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Preface
Thelastdecadehaswitnessedatremendousattentiondevotedtobothmodelingand
simulationofnonlineardynamicalsystems.Thishighinterestisduetothegrowing
awarenessthatnonlineardynamicsisinherentina vastclassofsystems, phenom-
enaandevents:naturalbiologicalsystems,physicalsystems,engineeringsystems,
etc. A study of the relevant state-of-the-artrevealsvarious scientific contributions
basedonmodeling,simulationandcontrolofnonlineardynamicalsystems.Various
interesting and striking states of these systems are of particular interest: periodic,
quasi-periodic, stable, unstable, deterministic, stochastic, synchronized, torus and
chaotic dynamics, etc. A good understanding and mastering of these states does
leadtovariouspotentialinterestingapplications.
Modelapproximationappearstobeaverycommonmodelingtechniqueinengi-
neeringsinceaccuratemodelsaregenerallyverycomplexandtoughtosolveeither
analyticallyorevennumerically.Further,itiswellknownthatnumericalsimulation
ispronetoaccumulationofround-offerrorsduringcomputation,whichcouldresult
intonon-realisticoutcomesespeciallyincaseofextremelystiffsystems.Numerical
simulationisalsoeventuallyverytime-consumingandsimulationconvergenceofis
notwell tractablesystematically.Thus,sometrade-offbetweenthe potentialanal-
ysis techniques appears necessary. Approximate models are easily solvable either
analyticallyor numericallyalthoughthe results obtainedare of less accuracy.Ac-
curatemodelingwhilemasteringrelatedcomputationalconcernsisindeedaserious
challengeformoderncomputationalengineering.
Thisbookisacollectionofrecentadvancedcontributionsinthefieldofnonlinear
dynamicsand synchronization,with special applicationsin the area of theoretical
electricalengineering.Thebookcontainstwenty-fourchaptersgroupedinfiveparts.
The first partconsisting of six chaptersdoesfocuson theoreticalissues related
to chaos and synchronizationand their potentialapplications in mechanics, trans-
portation,communicationandsecurity.Thesecondparthavingsixchaptershandles
dynamicsystemsmodelingandsimulationwithspecialapplicationstorealphysical
systemsandphenomena.Thethirdpartconsistingoffourchaptersdiscussessome
fundamentalsofelectromagnetics(EM)andaddressesthemodelingandsimulation
in some realphysicalelectromagneticscenarios. The fourth partof three chapters
VI Preface
doesmainlyaddressstabilityconcerns.Finally,thelastparthavingfourchaptersas-
semblessomesampleapplicationsintheareaofoptimization,datamining,pattern
recognitionandimageprocessing.
Inthefollowingthecontentsoftwenty-fourchaptersofthisbooksisrespectively
brieflypresented.
The first chapter, Synchronization of two nonidentical clocks: What Huy-
gens was able to observe?, by Krzysztof Czolczynski, Przemysław Perlikowski,
Andrzej Stefanski, and Tomasz Kapitaniak, addresses the synchronization of two
non-identicalclocks.Anin-depthanalyticalstudyiscarriedouttodemonstratethe
occurrenceofbothalmostcomplete(in-phase)andalmostanti-phasesynchroniza-
tions. These types of synchronizationare defined in terms of the phase shift. Evi-
denceisprovidedtoexplainthephenomenonofalmostanti-phasesynchronization
oftwopendulumclocksthatHuygenswasunabletoobserveexperimentallyinthe
XVIIthcentury.
Thesecondchapter,Onthesynchronizationof1Dand2Dmulti-scrollchaotic
oscillators,byJ.M.Mun˜oz-Pacheco,E.Zambrano-Serrano,O.G.Fe´lix-Beltra´n,E.
Tlelo-Cuautle, L.C. Go´mez-Pavo´n, R. Trejo-Guerra, A. Luis-Ramos, C. Sa´nchez-
Lo´pez, investigates synchronization issues in 1D and 2D multi-scroll chaotic os-
cillators. The applicabilityof these issues in communicationand security systems
is demonstrated.The 1D and 2D multi-scrollchaotic oscillators are simulated us-
ing the analog computingparadigm.A chaotic synchronizationscheme for multi-
directionalmulti-scrollchaosgeneratorsisintroducedandtheHamiltoniantheoryis
usedtoderivesynchronizationcriteria.Finally,twoschemesareset-uptotransmit
encrypted binary and analog signals by applying chaotic switching technique and
additive chaotic masking, respectively. Both schemes are also implemented using
analogcomputing.Thiscomputingparadigmissimulated/emulatedon.
The thirdchapter,Nonlinear filtering of chaosfor real-timeapplications, by
V. Kontorovich and Z. Lovtchikova investigates the nonlinear filtering of chaotic
signals in presence of additive white Gaussian noise (AWGN). Specifically, non-
linear filtering and chaotic phenomenaare investigatedwith concrete applications
in electrical engineering, basically in communications, control, etc. It is demon-
strated that both nonlinear and chaotic filtering are processes leading to various
potentialapplicationsincludingthosewhicharerelatedtoreal-timeregimecondi-
tions.Examplesoftheseapplicationsincludechaos-basedcommunicationssystems
synchronization, real-time control of chaos, radio-frequency interference filtering
andmitigation,andchaoticsystemidentification,justtonameafew.
Thefourthchapter,Time-of-flightestimationusingsynchronizedchaoticsys-
tems,byChristianF.WallingerandMarkusBrandnerdevelopsatheoreticalranging
concept based on time-of-flight(ToF) estimation. It is demonstrated that the con-
cept involving chaotic signal leads to various potential metrological applications.
A series of performance criteria for these applications are defined as fundamen-
tal parameters of the delay estimation process. An experimental demonstration is
describedshowingtheapplicabilityofsynchronizedchaoticsystemsinaToFmea-
surementsystem. Manytime-delaysare evaluated analyticallyand experimentally
andacomparisonisperformedtovalidatetheconceptsdeveloped.
Preface VII
Thefifthchapter,Binarysynchronizationofcomplexdynamicsincellularau-
tomataanditsapplicationsincompressedsensingandcryptography,byRadu
Dogaru and Ioana Dogaru applies a concept involving cellular automata to both
modeling and synchronization of complex dynamics. A specific focus is devoted
to the binarysynchronizationofthe transmittedbitstream.Itis demonstratedthat
the decodingof this stream is possible only when the structure of the cellular au-
tomata(encryptionkey)isknown.Finally,someapplicationsoftheconceptdevel-
oped are consideredin cryptography,spread spectrum communications,and com-
pressedsensing.Finally,animplementationoftheconceptonFPGAispresented.
Thesixthchapter, Self-ShapingAttractorsforCoupledLimitCycleOscilla-
tors,byJulioRodriguez,Max-OlivierHonglerandPhilippeBlanchardinvestigates
theissuesrelatedtobothsynchronizationandadaptationinnetworksofcoupled(or
interacting)limitcycleoscillatorseachofwhichischaracterizedbyitsfrequencies
and the shape of limit cycle. Specifically,the results obtainedshare light between
synchronizationandadaptationandthereforerevealthefundamentaldifferencebe-
tween them. In essence, an in-depth and systematic theoretical analysis is carried
outandsetsofanalyticalconditionsarederivedunderwhichthecoupledoscillators
are likely to exhibitbothsynchronized-and adaptive-dynamics.In particularit is
demonstratedthatthe self-adaptivemechanismultimately driveall oscillatorsto a
consensualdynamicalstate where all local systems share a common and constant
consensualsetofparameters.Theseparametersarecalculatedanalyticallyanditis
demonstrated that their values are independent of the network topology although
these values significantly affect the convergence rate. Therefore, interactions are
implementedviaacouplingmatrixwhosespectralpropertiescharacterizethecon-
vergenceconditionsleadingtoaconsensualstate.Finallynumericalsimulationsare
carriedouttovalidatetheanalyticalresults.
Theseventhchapter,Fastswitchingbehaviorinnonlinearelectroniccircuits:
a geometric approach, by Tina Thiessen, So¨ren Plo¨nnigs and Wolfgang Mathis
developsa geometric conceptto detect some striking and unexpectedbehavior of
aspecific classofnonlinearelectroniccircuits.Anexampleofthisbehavioristhe
fastswitchingbehaviorofcircuitswhichischaracterizedbythejumpsintheirstate
space.Ananalyticalstudyisdevelopedandappropriatecriteriaarederivedforthe
occurrence of jump conditions. The approach developed in this work is essential
as it allows a separation between the transientstates of the electronic circuits and
their permanent states. Finally, it is demonstrated that the geometric concept de-
veloped can easily be adapted to a system of equations based on MNA, allowing
animplementationoncircuitsimulatorssuchasSPICE.Numericalsimulationsare
consideredtovalidatetheanalyticalresultsdeveloped.
Theeighthchapter,DynamicsofLie´nardoptoelectronicoscillators,byBruno
Romeira,Jose´Figueiredo,CharlesN.IronsideandJulienJavaloyesinvestigatesthe
behavioranonlinearoptoelectronicoscillators(OEO)ofLie´nardtypes.Itisdemon-
stratedthattheeffectsduetonegativedifferentialresistanceacrossthetunneldiode
leadstooscillationswithinthesystem.Theconceptdevelopedinthischapterisvali-
datedbysomerecentexperimentalresultspresentedbytherelevantstate-of-the-art.
A specific focusis devotedto bothelectricalandopticalsystems, likely toexhibit
VIII Preface
complexdynamicsrangingfromself-sustainedrelaxationoscillations,to injection
lockingandchaoticdynamics.Potentialapplicationsoftheconceptinthischapter
are found in the developmentof secure communicationsystems and highly stabi-
lizedOEOdevicesformicrowave-photonicsystems.
The ninth chapter, Application of coupled dynamical systems for communi-
tiesdetectionincomplexnetworks,byNikolaiNefedov,modelsthe stablecom-
munities’detectionandlinkspredictionsprocessesincomplexnetworksbycoupled
ordinarydifferentialequations.Thedynamicsofthelocalstatesisdescribedbythe
well-knownKuramotomodel.Themethodisbasedonthedynamicalformulationof
modularityusingarandomwalkandthenisextendedtocoupleddynamicalsystems
todetectcommunitiesatdifferenthierarchicallevels.Bothattractiveandrepulsive
couplingareconsideredandtheireffectsonthedynamicsoftheglobalnetworkare
analyzed.Asproofofconceptsoftheapproachdevelopedinthechapter,practical
datasetsrecordedduringtheNokiamobile-datacollectioncampaignareconsidered
andtheconceptdevelopedisappliedtoderivethepotentialstructuresofthesocial
communityandtoperformlinkpredictionsorrecommendations.
Thetenthchapter,Infinitenetworksofhubs, spirals,andzig-zagpatternsin
self-sustainedoscillationsofatunneldiodeandofanerbium-dopedfiber-ring
laser, by Ricardo E. Francke, Thorsten Po¨schel, and Jason A.C. Gallas, investi-
gatesthedynamicsofanonlinearcircuitcontainingdiodesasanalogdevices.Some
strangeandoscillatingpatternsaredepictedanalyticallywhichcannotbeexplicitly
observed experimentally due to their appearance in a compressed form. To over-
comethisproblema circuitusinga tunneldiodeis designed.Thiscircuitislikely
to display two large spiral cascades over a wide range of parameter settings. It is
demonstratedthatsuchadisplaycanbeeasilyobservedexperimentally.
The eleventh chapter, Study of the dynamics of atmospheric pollution and
its association with environmental parameters, by Siwek Krzysztof, Osowski
Stanislaw, and Swiderski Bartosz investigates the dynamic processes of creation
ofatmosphericpollutionduetoSO2,NO2andozonepropagation.Theinterdepen-
dence between the pollution and the environmental atmospheric parameters (e.g.
temperature,wing,humidity,insolation,etc)isinvestigated.Itisdemonstratedthat
the interdependenceis nonlinear and could lead to chaotic dynamics. Finally, the
resultsofthesestudiesareexploitedinthedevelopmentofpredictionmodelsofthe
concentrationofparticularpollutants.
Thetwelfthchapter,Systemdynamicsmodelingofintelligenttransportation
systems - Human and social requirements for the construction of dynamic
hypotheses, by Oana Mitrea, structures the knowledge and requirements for the
(systemdynamics)modelingofdistributedactionsin theintelligenttransportation
systems from the perspective of the sociology of technology. This chapter con-
centrates on the potential of the theory of the distributiveness of actions in het-
erogeneous constellations (sociology of technology) to enhance the formulation
of dynamic hypotheses for system dynamics modeling of ITS. It is demonstrated
thatthe performanceof ITSsystems dependnotonly onthe interactivitybetween
the vehicle-humansystems and the environment,but also on the impact of socio-
politicalandothercontextualfactorsfromabroadersocio-technicalconstellation.
Preface IX
The thirteenth chapter, How to Handle Societal Complexity , by Dorien
DeTombe,developsafundamentalconceptprovidingasystematicapproachtocope
with complexsocietal problems. Examplesof these problemsare climate change,
the credit crisis, traffic dynamics, energy problems and pollution, just to name a
few. In essence the most important contribution of this chapter is concerned with
the enrichment of the state-of-the-art regarding the modeling of complex societal
problems.Indeed,theclassicalmethodsarebasedonPolicymakers.However,most
policymakersareneithereducatednorcapable,andoftenunwillingtohandlethese
problemsinthemostoptimalwayinordertoreachsustainablechanges.Therefore,
A scientific methodology for handling complex societal problems, the so-called
Compram(complexproblemhandlingmethod)isdevelopedinthefieldofMethod-
ology of Societal Complexity. It is demonstrated that applying this methodology
leadstomorerobust/stableandsustainablechangesinsituationscausedbycomplex
societalproblems.
Thefourteenthchapter,Fundamentalsofelectrodynamics,byBrankoMisˇkovic,
developssomefundamentalbasicsoftheelectromagnetics(EM)theory.Somelights
are shed on important basic aspects of the EM theory which were not clearly ex-
plainedbytherelevantliterature.ThisisachievedconsideringthreeclassesofEM
quantities namely, electric charges, currents, and kinetic magnetic fields. A new
mathematicalexpressionofthegeneralkineticcentrallawisderivedusingthecon-
ceptdevelopedinthischapter.Further,thesecondaryfieldtransformationsarealso
completed. The relativistic postulates and respective kinematical transformations,
basedontheincompletefieldtransformations,arefinallydisqualified.Ontheother
hand,Einstein’sequationandLorentz’mass functionare explainedand validated.
Thecircularspatialaxesarealsoexplainedandvalidatedbythewavecosmicpro-
cess, which determines by itself gravitationalattraction, with unique and uniform
lapseoftime,inagreementwiththeGalileanview.
The fifteenth chapter, Advanced adaptive algorithms in 2D finite elements
method of higher order of accuracy, by Pavel Karban, Ivo Dolezˇel, Frantisˇek
Mach, and Bohusˇ Ulrych develops a new method for automatic adaptivity in fi-
niteelementmethodsofhigherorderofaccuracy.Themainattentionisdevotedto
hp-adaptivity techniques that exhibit the highest level of flexibility and exponen-
tialconvergenceofresults.ThetechnologiesareimplementedintheadaptiveFEM
codesandfinallybothAgros2DandHermes2Dbasedonahigher-orderfiniteele-
mentmethodareillustratedbythreetypicalexamples.
Thesixteenthchapter,SPICEmodelforfasttimedomainsimulationofpower
transformers, exploiting the ferromagnetic hysteresis and eddy-currents, by
LucianMandache,DumitruTopan,MihaiIordache,andIoanaGabrielaSirbu,con-
sidersbothmodelingandsimulation(usingSPICE)ofpowertransformers.Specific
states are depicted, namely saturation regime, static hysteresis and eddy currents.
The principle of magnetic circuit modeling is based on analog lumped equivalent
circuitsandtheSPICEimplementationusestheprincipleofmodularity.Itisdemon-
strated that the method developedin this chapter allows simulation of normalop-
eration modes, as well as critical transients and faulty conditions.A case study is
X Preface
presentedtoprovethefeasibility,usefulnessandaccuracyoftheproposedmodeling
and simulation approach, where the SPICE results are validated by experimental
ones.
The seventeenth chapter, Hard-coupled modeling of induction shrink fit of
gas-turbine active wheel, by Va´clav Kotlan, Pavel Karban, Bohusˇ Ulrych, Ivo
Dolezˇel, and Pavel Kus, develops a hard-coupled model of induction heating of
a ferromagneticdisk. The mathematicalmodelis derivedfrom three coupled par-
tialdifferentialequations(forthedistributionofelectromagneticfield,temperature
fieldandfieldofthermo-elasticdisplacements)whosecoefficientsaretemperature-
dependentfunctions.ThefiniteelementmethodisimplementedintotheHermesand
Agroscodesand numericalsolutionsareobtained.The methodologyis illustrated
by a typical example, i.e., heating of an active wheel of a high-speed gas turbine
that is to be hot-pressedon a shaft with the aim of obtaininga shrink fit allowing
transferringthe giventorque at the nominalrevolutions.Finally the parametersof
theheatingprocessintransverseandlongitudinalmagneticfieldsareevaluatedand
discussed.
Theeighteenthchapter,Stabilityanalysisandlimitcyclesofhighordersigma-
delta modulators, by Valeri Mladenov, considers the stability analysis of limit
cycle oscillations in a one bit high order sigma-delta modulators. An approach is
developedandappliedtosigma-deltamodulatorsasageneralanalysisframework.
Theapproachdevelopedisbasedonaparalleldecompositionofthemodulatorand
a direct nonlinear systems analysis. In this representation, the general N-th order
modulator is transformed into a decomposition of low order, generally complex
modulators,whichinteractonlythroughthequantizerfunction.
Thenineteenthchapter,Stabilityanalysisofvectorequalizationbasedonre-
current neural networks, by Mohamad Mostafa, Werner G. Teich, and Ju¨rgen
Lindner,focusesonanapplicationofRNNsincommunicationsengineering,namely
the vectorequalization.Theimportanceof thisprocedurearisesfromthe factthat
thereisnoneedfortraining.TheparametersoftheRNNtoactasvectorequalizer
can be obtained by investigatingthe stability properties of these networks and by
choosingasuitableactivationfunction,whichisthecoreofthiswork.Bothglobal
andlocalstabilityofthediscrete-timeandcontinuous-timeRNNinthecontextofa
vectorequalizerareanalyzedandtheimpactofthestabilityconditionsontheequal-
izationprocessis depicted.Itisshownthatthe globalstabilityis interestingif the
weightmatrix is not symmetric. Finally, it is demonstratedthat a vectorequalizer
basedonRNNswithincreasingslopeoftheactivationfunctionduringtheiteration
processcanbeinterpretedasaschemewithatransitionfromglobalstabilitytolocal
stability.
The twentieth chapter, Stability of linear circuits with interval data: a case
study, by ZygmuntA. Garczarczykanalysesthe stability of a linear lumpedelec-
tric circuit with interval data that modeluncertainties of their element parameters
(passiveelementvaluesR,L,Candcontrolledsourcecoefficientsk).Anapproach
is developedbasedon the checkingof the stability of a symmetricintervalmatrix
associatedwiththestatematrixandonsomeintervalanalysisresults.Themethodis