Monotone Dynamics.pdf

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1、MonotoneDynamicalSystemsM.W.HirschHalSmithyNovember22,2004Contents0Introduction31StronglyOrder-PreservingSemi ows61.1DenitionsandBasicResults........................61.2NonorderingofOmegaLimitSets......................121.3LocalSemi ows................................141.4TheLim

2、itSetDichotomy..........................151.5Qisplentiful.................................181.6StabilityinNormallyOrderedSpaces....................211.7StableEquilibriainStronglyOrderedBanachSpaces...........241.8TheSearchforStableEquilibria.......................272GenericConverg

3、enceandStability302.1TheSequentialLimitSetTrichotomy....................302.2GenericQuasiconvergenceandStability...................362.3ImprovingtheLimitSetDichotomyforSmoothSystems.........372.4GenericConvergenceandStability.....................443OrdinaryDierentialEquations473.

4、1TheQuasimonotoneCondition........................483.2StrongMonotonicity.............................513.3AutonomousK-CompetitiveandK-CooperativeSystems.........553.4DynamicsofCooperativeandCompetitiveSystems............573.5Smale'sConstruction.............................60Depa

5、rtmentofMathematics,UniversityofCalifornia,Berkeley,CA94720-3840.SupportedbyNSFGrantDMS9700910yDepartmentofMathematics,ArizonaStateUniversity,Tempe,AZ85287-1804.SupportedbyNSFGrantDMS010716013.6InvariantSurfacesandtheCarryingSimplex................6123.7SystemsinIR................

6、.................6233.8SystemsinIR.................................634DelayDierentialEquations694.1TheSemi ow.................................694.2TheQuasimonotonecondition........................704.3EventualStrongMonotonicity........................744.4KisanOrthant............

7、....................774.5GenericConvergenceforDelayDierentialEquations...........795MonotoneMaps815.1BackgroundandMotivatingExamples...................815.2DenitionsandBasicResults........................835.3TheOrderIntervalTrichotomy.......................875.4Sublinearityandt

8、heConeLimitSetTrichotomy.........