Table Of ContentNonlinear 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
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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
