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1、PHYSICALREVIEWLETTERSweekendingPRL101,084103(2008)22AUGUST2008SolvableModelforChimeraStatesofCoupledOscillatorsDanielM.Abrams,1RennieMirollo,2StevenH.Strogatz,3,*andDanielA.Wiley41DepartmentofEarth,Atmospheric,andPlanetarySciences,54-621,MassachusettsInstituteofTechnology,
2、Cambridge,Massachusetts02139,USA2DepartmentofMathematics,BostonCollege,ChestnutHill,Massachusetts02467,USA3DepartmentofTheoreticalandAppliedMechanics,CornellUniversity,Ithaca,NewYork14853,USA4DepartmentofMathematics,UniversityofMaryland,CollegePark,Maryland20742,USA(Receiv
3、ed3June2008;published22August2008)Networksofidentical,symmetricallycoupledoscillatorscanspontaneouslysplitintosynchronizedanddesynchronizedsubpopulations.Suchchimerastateswerediscoveredin2002,butarenotwellunderstoodtheoretically.Hereweobtainthefirstexactresultsaboutthestabi
4、lity,dynamics,andbifurcationsofchimerastatesbyanalyzingaminimalmodelconsistingoftwointeractingpopulationsofoscillators.Alongwithacompletelysynchronousstate,thesystemdisplaysstablechimeras,breathingchimeras,andsaddle-node,Hopf,andhomoclinicbifurcationsofchimeras.DOI:10.1103
5、/PhysRevLett.101.084103PACSnumbers:05.45.XtManycreaturessleepwithonlyhalftheirbrainatatimecoupledequallytoalltheothersinitsgroup,andless[1].Suchunihemisphericsleepwasfirstreportedindol-stronglytothoseintheothergroup.Forthismodelwephinsandotherseamammals,andhasnowbeenseenins
6、olveforthestationarychimerasanddelineatewheretheybirdsandinferredinlizards[2].Whenbrainwavesareexistinparameterspace.Anunexpectedfindingisthatrecorded,theawakesideofthebrainshowsdesynchron-chimerasneednotbestationary.Theycanbreathe.Thenizedelectricalactivity,correspondingto
7、millionsofneu-thephasecoherenceinthedesynchronizedpopulationronsoscillatingoutofphase,whereasthesleepingsideiswaxesandwanes,whilethephasedifferencebetweenthehighlysynchronized.twopopulationsbeginstowobble.Fromaphysicist’sperspective,unihemisphericsleepThegoverningequations
8、forthemodelaresuggeststhefollowing(admittedly,extremelyidealized)X2XN0problem:What’sthe
