该【An approach of the exact linearization techniques to analysis of population dynamics of the mosquito Aedes aegypti Célia A. dos Reis 】是由【探春文档】上传分享,文档一共【22】页,该文档可以免费在线阅读,需要了解更多关于【An approach of the exact linearization techniques to analysis of population dynamics of the mosquito Aedes aegypti Célia A. dos Reis 】的内容,可以使用淘豆网的站内搜索功能,选择自己适合的文档,以下文字是截取该文章内的部分文字,如需要获得完整电子版,请下载此文档到您的设备,方便您编辑和打印。:..,,DiegoC?olon,?,?PII:S0025-5564(17)30172-4DOI:.:MBS8008Toappearin:MathematicalBiosciencesReceiveddate:29March2017Reviseddate:29September2017Accepteddate:8December2017Pleasecitethisarticleas:,,DiegoC?olon,?,,ANAPPROACHOFTHEEXACTLINEARIZATION?TECHNIQUESTOANALYSISOFPOPULATIONDYNAMICSOFTHEMOSQUITOAedesaegypti,MathematicalBiosciences(2017),doi:.,typesetting,,andalllegaldisclaimersthatapplytothejournalpertain.:..ACCEPTEDMANUSCRIPTHighlights?Theanalyzingviaexactlinearizationtechniquesofasystemdescribingthepopulationdynamicsofaedesaegyptiwasproposed.?Weproposedthedesignofacontrollawforthevectorcontrolpopulation.?WeproposedaVNS(Variableneighborhoodsearch)AlgorithmtodetermineoptimalcontroloftheAedesaegyptipopulation.?VNSiseasytoimplementandhasprovedagoodtoolfordeterminingoptimumcontrols.?:..ACCEPTEDMANUSCRIPTANAPPROACHOFTHEEXACTLINEARIZATIONTECHNIQUESTOANALYSISOFPOPULATIONDYNAMICSOFTHEMOSQUITOAedesaegypti1234Cé,,DiegoCólon,Sué,ática,FC,UNESP,17033-360,Bauru,SP,BrazilE-mail:******@ística,IB,UNESP18618-670,Botucatu,SP,BrazilE-mail:******@-PTC,POLI,USP05508-900,S?oPaulo,SP,BrazilE-mail:******@íliaUnB,BrazilE-mail:******@,,theinfectioncanhavedevastatingeffects,affectingthecentralnervoussystem,muscles,brainandrespiratorysystem,,therefore,currentstudiesarefocusedonthetreatmentofdiseasesandvector(mosquito),andpresentstheanalysisofamathematicalmodeldescribingthepopulationdynamicsofAedesaegypti,aswellaspresentthedesignofacontrollawforthemosquitopopulation(vectorcontrol),:Aedesaegypti,dynamicmodel,exactlinearizationtechniques,dengue,chikungunya,,theirresistance,adaptabilityand2:..ACCEPTEDMANUSCRIPTproximityofhumanpopulations,,theAedesaegyptitransmitsvirusesthatcausedenguefever,chikungunyaandzika[1].Denguefeveriscausedbyanarbovirusoftheflaviviridaefamily,whichincludesfivevirusserotypes,calledDEN1,DEN2,DEN3,,headache,-threateningdisease,,,,orsimplyzika,,and,whenpresent,,mother-to-,itwasobservedalargenumberofcasesinchildrenthatwerebornwithmicrocephalyinBrazil,whichwereassociatedwiththemother'sinfectionbyzikavirus,–Barrésyndrome(GBS),[2-4].ineandnospecifictreatmentforthesediseases,thereforethetechniquesofvectorpopulationcontrolarewidelyused,thoughnotalwayseffectively,whetherforreasonsofenvironmentalcontaminationofchemicalcontrolsorthehighostofthebiological,,itisnecessarytounderstandthepopulationdynamicsofthemosquito[1,5].Inthiswork,weproposetostudythepopulationdynamicsofAedesaegyptimosquitoesandapplyvectorcontroltechniquesfortheaquaticpopulationphaseofthemosquitoes(thatareegg,larvaandpupa,withinterventionsforreductionofaquaticpopulation).TheACCEPTEDMANUSCRIPTmathematicalmodeladdressedhereisbasedin[6],andweproposedtoapplythetechniqueofexactfeedbacklinearizationtolinearizethisnonlinearmodel,:..ACCEPTEDMANUSCRIPTTheexactfeedbacklinearizationisaprocedurethatcantransformthedynamicsofanonlinearsysteminalineardynamicsthroughanonlinearfeedbackofthestatesoroutputs(thatarefunctionsofthestates).Furthermore,itisanessentialpartforthedevelopmentofnonlinearrobustandadaptivecontrollers[7-9].essfullyinawiderangeofapplications,suchastrackingproblems,controlofrobotarmsandmanipulators,artillery,helicopters,airplanesandsatellites,moreover,hasbeenusedinmedicalequipment,pharmaceuticalandchemicalindustries[7,9,10,11].,,thetwoopenloopequilibriumpointsaredetermined,,,,(periodsofintensesunlight)or3weeks(coldperiods),prisesfourstages:egg,larva,,foodavailabilityandquantityoflarvaeinbreeding,andcanbedividedintotwophases:aquaticphase(egg,larvaandpupa)andterrestrialphase(adultstage).Infavorableenvironmentalconditions,aftertheegghatching,,:..ACCEPTEDMANUSCRIPTFigure1:LifecycleofAedesaegypti:aquaticphase(larvae,pupae,eggs)andterrestrialphase(adults).,,suchasyellowfever,denguefever,,andthepopulationcontrolisdifficultduetoitsversatilityinthechoiceofbreedingtolayitseggs,andtheextremelyeggs’resistance(esavailabletoprovidesincubation).Onceimmersed,theeggsdeveloprapidlyintolarvae,whichgiverisetopupae,fromwhichtheadultemerges[5].Aimingtoassistthestudyandunderstandingthebehaviorofthemosquitopopulationdynamics,,,basedon[6],wepresentthemathematicalmodelinEquation(1)describingthepopulationdynamicsofmosquitoes:ACCEPTEDMANUSCRIPT????x?1??(???1)x1??x3????x1x3?x1u(t)??C????x?2?r?x1?????2?x2,?(1)x?3??x2??3x3?????x?4??1?r??x1??4x45:..ACCEPTEDMANUSCRIPTwherex1(t)isthedensityofindividualsoftheaquaticpopulationphase(eggs,larvaeandpupae),x2(t)isthedensityofindividualsoftheimmaturefemalespopulation(beforemating),x3(t)isthedensityofindividualsofthefertilizedfemalespopulation(aftermating)andx4(t)thedensityofmaleindividuals(naturalmale).Mortalityratesassociatedwitheachsegmentofthepopulation(water,immaturefemales,fertilizedfemalesandmales)arerespectivelydenotedbyμ1,μ2,,whichisgivenby?x1?beingthe?????1?C????rateofintrinsicovipositionandCmeanstheenvironmentalcapabilityrelatedtothenumberofnutrients,space,,andaratiordevelopinfemalesand(1-r)(t)actsasatime-varyingmortalityrate,,thefollowingchangesintheModel(1)areproposed:A1??(???1),?,A3?r?,A4??(???2),A5?(1?r)?.A2??CThenthesystemofEquations(1)canbewrittenas:?x?1??A1x1??x3?A2x1x3???x1???????x?2A3x1?A4x20????????u(t),(2)?x?3???x2??3x3??0????????x?4??A5x1??4x4??0???f(x)?g,(x)u(2a)where,?x?1??A1x1??x3???xA1?2x1x3???????x?2A3x1?A4x20x????,f(x)??,g(x)???andu=u(t?).(2b)?x?3???x2??3x3?0????????ACCEPTEDMANUSCRIPT?x?4??A5x1??4x4?0??,paredwithclassicalTaylorserieslinearization(orJacobian),isthatfeedbacklinearizationisglobal,:..ACCEPTEDMANUSCRIPTtoallstatespacedomainoroutput,withthepossibleexceptionofisolatedpoints,whiletheTaylorserieslinearizationislocal,.,,whiletheJacobianlinearizationisapproximated,thefeedbacklinearizationisexact[7-9].Wealsoconsiderthatanoutputvariabley=h(x),thatisafunctionofthestates(populationdensities),canbemeasuredinreal-timebysomeway(usingsensors).Thus,themathematicalmodelisofSISO(singleinputsingleoutput)type,andispresentedinEquation(3)below:x??f(x)?g(x),u(3)y?h(x)nwherex??isastatevector,u??isthecontrolinput,f,g:D??n?aresmooth?nvectorfieldsinD??,therearetwomainmethods:input-to-statelinearizationandinput-to--outputlinearizationistotransformthenonlineardynamicsystem(3)inthesocallednormalform,thatis,alinearouterpart(input-outputsub-model)andanonlinearinnerandnon-observablepart(alsocalledinternaldynamic).Forthispurpose,anewsetofstatesisdefined(thataretheoutputyanditstimederivatives)andtheexistenceofadiffeomorphism,whichtransformsthenonlinearsysteminanotherlinearsystem,?z1,...,y(r)?zr,-outputlinearizationcorrespondsto(n–r)equationsoftheform???w(z,?)andispartofthenormalform,,
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