Advances in Dynamics, Patterns, Cognition: Challenges in Complexity PDF
Preview Advances in Dynamics, Patterns, Cognition: Challenges in Complexity
Nonlinear Systems and Complexity Series Editor: Albert C.J. Luo Igor S. Aranson Arkady Pikovsky Nikolai F. Rulkov Lev S. Tsimring Editors Advances in Dynamics, Patterns, Cognition Challenges in Complexity Nonlinear Systems and Complexity Volume 20 Serieseditor AlbertC.J.Luo SouthernIllinoisUniversity Edwardsville,IL,USA Nonlinear Systems and Complexity provides a place to systematically summarize recentdevelopments,applications,andoveralladvanceinallaspectsofnonlinearity, chaos, and complexity as part of the established research literature, beyond the novel and recent findings published in primary journals. The aims of the book seriesaretopublishtheoriesandtechniquesinnonlinearsystemsandcomplexity; stimulate more research interest on nonlinearity, synchronization, and complexity in nonlinear science; and fast-scatter the new knowledge to scientists, engineers, and students in the corresponding fields. Books in this series will focus on the recent developments, findings and progress on theories, principles, methodology, computational techniques in nonlinear systems and mathematics with engineering applications. The Series establishes highly relevant monographs on wide ranging topics covering fundamental advances and new applications in the field. Topical areasinclude,butarenotlimitedto:NonlineardynamicsComplexity,nonlinearity, and chaos Computational methods for nonlinear systems Stability, bifurcation, chaos and fractals in engineering Nonlinear chemical and biological phenomena FractionaldynamicsandapplicationsDiscontinuity,synchronizationandcontrol. Moreinformationaboutthisseriesathttp://www.springer.com/series/11433 Igor S. Aranson • Arkady Pikovsky Nikolai F. Rulkov • Lev S. Tsimring Editors Advances in Dynamics, Patterns, Cognition Challenges in Complexity 123 Editors IgorS.Aranson ArkadyPikovsky PennsylvaniaStateUniversity InstituteforPhysicsandAstronomy UniversityPark,PA,USA UniversityofPotsdam Potsdam,Germany NikolaiF.Rulkov BioCircuitsInstitute LevS.Tsimring UniversityofCaliforniaSanDiego BioCircuitsInstitute LaJolla,CA,USA UniversityofCaliforniaSanDiego LaJolla,CA,USA ISSN2195-9994 ISSN2196-0003 (electronic) NonlinearSystemsandComplexity ISBN978-3-319-53672-9 ISBN978-3-319-53673-6 (eBook) DOI10.1007/978-3-319-53673-6 LibraryofCongressControlNumber:2017936388 ©SpringerInternationalPublishingAG2017 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.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Thisbookisdedicatedtothe75thbirthdayof MichaelRabinovich,apioneerofnonlinear science Preface: Misha Rabinovich and Nonlinear Dynamics in the Last Half-Century ПОЗНАНИЕ Узлами скручены спирали, А между ними судеб путь. Скопленья звезд спираль порвали, Хотя б вполглаза мне взглянуть, Потрогать грань меж Раем - Адом, Порядок в хаосе понять, Услышать рев галактик рядом И... Богом все это назвать. Михаил Рабинович COGNITION Spiralsarewrungintoknots. BetweenthemliesthewayoftheFates. Starclustersoncetorethespirals. Oh,ifIcouldglimpseevenhalfofthis, TouchthethinbetweenHeavenandHell, PerceiveOrderinChaos, Heartheroarofgalaxiesnextdoor, And–tocallitGod:allofit. MikhailRabinovich (EnglishtranslationbyOlgaLivshin) This book is comprised of contributions by just a few of a very large cohort of friends, colleagues, and former students of Misha Rabinovich or, as he is often affectionally called after his initials, MIR.1 In the last half-century, Misha 1ThewordmirmeansbothpeaceandworldinRussian. vii viii Preface:MishaRabinovichandNonlinearDynamicsintheLastHalf-Century Rabinovich has been at the forefront of most major developments in nonlinear dynamics, starting from the development of asymptotic methods for the analysis ofnonlinearwavesinnon-equilibriummediatothepresentdayswhenheisusing nonlinear dynamics toadvance thetheoryofcognition.Inthesebriefintroductory notes,wewillattempttosketchMisha’sportraitbothasascientistandasahuman beingandconnectitwiththecontentsofthisbook. MikhailIzrailevichRabinovichwasbornonApril20,1941,inNizhnyNovgorod (thenGorky)inthefamilyofIsraelRabinovich,aprofessorofchemistryatGorky State University. In his teenage years, Misha was an avid cross-country skier and onlygotseriousaboutsciencetowardthesecondhalfofhisuniversitystudies.But inscience,justasearlierinsports,hewasveryfastandnotonlyquicklycaughtup withhispeersbutleftthemfarbehind. MIR got his first taste of doing research around 1960 during his sophomore universityyearinthefieldwhichnowiscalledrobotics.Hisfirstscientificmentor Tyoma Alekseev suggested to him a student project to improve the efficiency of a conveyor at Gorky Automobile Plant (GAZ). Before long, Misha developed an automationalgorithmandimplementeditatoneoftheplantconveyors.Thatwork not only led to increased efficiency of the conveyor operation and caused some layoffs, but italsobecame his firstpublished paper. However, MIRdecided not to pursuehisscientificcareerinroboticsandswitchedtothenonlineardynamicsand theoreticalphysics.Nevertheless,thisshortstintatGAZpossiblyplayedabigrole in his future scientific development.2 While MIR has always been a theorist, he is also known for deep understanding of experiment, often suggesting original ideas tohisexperimentalcolleagues. Hewasonly26whenin1967hedefendedhiscandidateofphysicalandmathe- maticalsciences’dissertation(ananalogofPh.D.thesisintheWest),andat33he alreadyobtainedthedoctorofsciencedegree(ananalogofhabilitationinGermany, exceptionallyearlybySovietstandards).In1991,hewaselectedthecorresponding memberoftheRussianAcademyofSciences.Thegeneraldirectionofhisscientific studiesfromthoseveryearlydayshasremainedthetheoryofnonlinearoscillations and waves. This was quite natural for him, perhaps even unavoidable, because he belongs to the illustrious school of nonlinear dynamicists established by Leonid MandelshtamandhisstudentsAlexanderAndronov,GabrielGorelik,andMikhail Leontovich, followed among others by Misha’s Ph.D. adviser Andrey Gaponov- Grekhov. This scientific dynasty is widely known not only for their fundamental discoveries in physics of oscillations and waves but also for applying them in practice,rangingfromclockstopowerfulgeneratorsofelectromagneticoracoustic radiation. OneofMishaRabinovich’sfirstsignificantcontributionstononlineardynamics was the theoretical discovery of stable stationary waves in active nonlinear media inthelate1960s.Thefirstexperimentalstudieswereperformedwiththechainsof 2ThisearlyphaseofMIR’sscientificcareerisnotwelldocumented,andouraccountofitismostly basedonourmanyfriendlyeveningconversations. Preface:MishaRabinovichandNonlinearDynamicsintheLastHalf-Century ix coupled electronic self-sustained oscillators [6]. These stable nonlinear structures werelaterfoundinplasmaphysicsandfluiddynamicsandwereusedinlasersand networksofradiofrequencyoscillators.Ataboutthesametime,hewithhisPh.D. student Alexander Rosenblum (who was 15 years older than MIR) proposed an asymptoticmethodfortheoreticalanalysisofself-sustainedoscillationswhichwas anontrivialextensionoftheclassicalKrylov-Bogolyubovasymptoticmethodtothe distributednonlinearsystems[16]. Perhaps it is Misha’s extremely active persona that always attracted him to non-equilibrium systems and nonlinear dynamics. In 1972, he discovered a novel phenomenon of explosive instability in the nonlinear interaction of waves in non-equilibriummedia.Inthissituationtheamplitudesofallthreewaysgrowsuper- exponentiallyandbecomeinfiniteinafinitetimeunlesshigher-ordernonlinearities limit their growth [15]. When the new Institute of Applied Physics of the Soviet Academy of Sciences opened its doors in 1977, MIR became the head of the Laboratory for Nonlinear Dynamics and Chaos which quickly became one of the centersofnonlineardynamicsintheSovietUnion.Manyofhisstudentsandjunior collaborators (including editors and a large fraction of authors of this volume) workedinthislaboratoryandbenefitedfromdailyinteractionswithMIR.However, hisroleingroominggenerationsof“nonlineardynamicists”isevengreater.Misha hasalwaysbeenawonderfulteacherandmentor.AsaprofessoroftheGorkyState University,heestablishedayearlonglecturecourseonthetheoryofoscillationsand waves and taught it himself every year for 30 years. This class was the highlight of our own years at the radiophysics department of the Gorky State University in the 1970s. This nonlinear dynamics course laid the foundation of the popular textbookwrittenbyhimincollaborationwithDmitryTrubetskov[18].Hisanother crown achievement was establishing and running famous “Schools on Nonlinear OscillationsandWaves”thatwereheldbiannuallyinabeautifulcountrysidesome 200km from Gorky. These 2-week-long springtime gatherings brought together famous physicists and mathematicians (V.I. Arnold, B.B. Kadomtsev, Ya.I. Sinai, Ya.B. Zeldovich, and many others) and hundreds of young researchers in a very informalandstimulatingatmosphere.Thistraditionsurvivedeventhedemiseofthe SovietUnionandcontinuestothisday;thenextschoolisplannedfor2018. Inthe1970–1980s,MishaRabinovichturnedhisattentiontodeterministicchaos and pattern formation. They were nascent fields at the time, and Misha was one oftheearlypioneers.Inhis1979paperwithhisformerstudentAnatolyFabrikant [13], they demonstrated the emergence of low-dimensional deterministic chaos in a spatiotemporal system describing modulational instability of nonlinear waves in dissipativemedia.Theyreducedthisinfinite-dimensionalproblemtoasetofthree ordinary differential equations now known as “Rabinovich-Fabrikant equations.” In 1980, MIR with Sergey Kiyashko and one of us demonstrated deterministic chaos in a simple electronic circuit [7]. His influential 1978 review in “Soviet
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