matcont and cl matcont实验教程1.pdf

文档介绍：tutoriali:,UtrechtSeptember19,20111Thissessionillustrateshowtoinputasystemofautonomousordinarydifferentialequations(ODEs)nmx˙=f(x,α),x∈R,α∈R,intomatcontandnumericallyintegrateitwithsimultaneouslyvisualizingorbitsingraphicwin-¨osslerchaoticsystem:x˙=−y−zy˙=x+Ayz˙=Bx−Cz+xz,where(x,y,z)arethephasevariables,and(A,B,C)-stalledproperly(pilationoftheC-filesinthesubdirectoryLimitCycle;fordetailssee§“MATCONTandCLMATCONT:ContinuationtoolboxesinMATLAB,versionofAugust2011).:“adapt2”,,toendyourmatcontsession,|,|System|NewopenstheSystemwindow,,typeforexampleRosslerintheNamefield(itmustbeoneword).InputnamesoftheCoordinates:X,Y,Z,theParameters:AA,,andthenameforTime:t(default).Ifshown,selectsymbolicgenerationofthe1storderderivativesbypressingthecorrespondingradio-:,inthelargeinputfield,typetheRHSofR¨ossler’ssystemas1IftheMATLABSymbolicToolboxispresent,therewillbebuttonsindicated’symbolically’.Thefirst-orderderivativesareusedinsomeoftheintegrationalgorithms,thefirst-andsecond-orderderivativesareusedinthecontinuation,whilethethird-’=-Y-ZY’=X+AA*YZ’=BB**Z+X*ZAvoidtypicalmistakes:•Somenames()arereservedinMATLABandcannotbeused.•Donotputspacesbetweencoordinateandparameternames.•Makesurethemultiplicationiswrittenexplicitlywith∗.•