实用分歧和稳定性分析影印版（第2版）

Preface
Notation
1IntroductionandPrerequisites
1.1ANonmathematicalIntroduction
1.2StationaryPointsandStability(ODEs)
1.2.1TrajectoriesandEquilibria
1.2.2Deviations
1.2.3Stability
1.2.4LinearStability;DufiingEquation
1.2.5DegenerateCases;ParameterDependence
1.2.6Generalizations
1.3LimitCycles
1.4Waves
1.5Maps
1.5.1OccurrenceofMaps
1.5.2StabilityofFixedPoints
1.5.3CellularAutomata
1.6SomeFundamentalNumericalMethods
1.6.1Newton'sMethod
1.6.2IntegrationofODEs
1.6.3CalculatingEigenvalues
1.6.4ODEBoundary-ValueProblems
1.6.5FurtherTools
2BasicNonlinearPhenomena
2.1APreparatoryExample
2.2ElementaryDefinitions
2.3BucklingandOscillationofaBeam
2.4TurningPointsandBifurcationPoints:TheGeometricView
2.5TurningPointsandBifurcationPoints:TheAlgebraicView
2.6HopfBifurcation
2.7BifurcationofPeriodicOrbits
2.8ConvectionDescribedbyLorenz'sEquation
2.9HopfBifurcationandStability
2.10GenericBranching
2.11BifurcationinthePresenceofSymmetry
3PracticalProblems
3.1ReadilyAvailableToolsandLimitedResults
3.2PrincipalTasks
3.3WhatElseCanHappen
3.4MarangoniConvection
3.5TheArtandScienceofParameterStudy
4PrinciplesofContinuation
4.1IngredientsofPredictor-CorrectorMethods
4.2Homotopy
4.3Predictors
4.3.1ODEMethods;TangentPredictor
4.3.2PolynomialExtrapolation;SecantPredictor
4.4Parameterizations
4.4.1ParameterizationbyAddinganEquation
4.4.2ArclengthandPseudoArclength
4.4.3LocalParameterization
4.5Correctors
4.6StepControls
4.7PracticalAspects
5CalculationoftheBranchingBehavior
ofNonlinearEquations
5.1CalculatingStability
5.2BranchingTestFunctions
5.3IndirectMethodsforCalculatingBranchPoints
5.4DirectMethodsforCalculatingBranchPoints
5.4.1TheBranchingSystem
5.4.2AnElectricalCircuit
5.4.3AFamilyofTestFunctions
5.4.4DirectVersusIndirectMethods
5.5BranchSwitching
5.5.1ConstructingaPredictorviatheTangent
5.5.2PredictorsBasedonInterpolation
5.5.3CorrectorswithSelectiveProperties
5.5.4SymmetryBreaking
5.5.5CoupledCellReaction
5.5.6ParameterizationbyIrregularity
5.5.7OtherMethods
5.6MethodsforCalculatingSpecificBranchPoints
5.6.1ASpecialImplementationfortheBranchingSystem
5.6.2RegularSystemsforBifurcationPoints
5.6.3MethodsforTurningPoints
5.6.4MethodsforHopfBifurcationPoints
5.6.5OtherMethods
5.7ConcludingRemarks
5.8Two-ParameterProblems
6CalculatingBranchingBehavior
ofBoundary-ValueProblems
6.1EnlargedBoundary-ValueProblems
6.2CalculationofBranchPoints
6.3SteppingDownforanImplementation
6.4BranchSwitchingandSymmetry
6.5TrivialBifurcation
6.6TestingStability
6.7HopfBifurcationinPDEs
6.8HeteroclinicOrbits
7StabilityofPeriodicSolutions
7.1PeriodicSolutionsofAutonomousSystems
7.2TheMonodromyMatrix
7.3ThePoincareMap
7.4MechanismsofLosingStability
7.4.1BranchPointsofPeriodicSolutions
7.4.2PeriodDoubling
7.4.3BifurcationintoTorus
7.5CalculatingtheMonodromyMatrix
7.5.1APosterioriCalculation
7.5.2MonodromyMatrixasaBy-ProductofShooting
7.5.3NumericalAspects
7.6CalculatingBranchingBehavior
7.7PhaseLocking
7.8FurtherExamplesandPhenomena
8QualitativeInstruments
8.1Significance
8.2ConstructionofNormalForms
8.3AProgramTowardaClassification
8.4SingularityTheoryforOneScalarEquation
8.5TheElementaryCatastrophes
8.5.1TheFold
8.5.2TheCusp
8.5.3TheSwallowtail
8.6Zeroth-OrderReactioninaCSTR
8.7CenterManifolds
9Chaos
9.1FlowsandAttractors
9.2ExamplesofStrangeAttractors
9.3RoutestoChaos
9.3.1RouteviaTorusBifurcation
9.3.2Period-DoublingRoute
9.3.3Intermittency
9.4PhaseSpaceConstruction
9.5FractalDimensions
9.6LiapunovExponents
9.6.1LiapunovExponentsforMaps
9.6.2LiapunovExponentsforODEs
9.6.3CharacterizationofAttractors
9.6.4ComputationofLiapunovExponents
9.6.5LiapunovExponentsofTimeSeries
9.7PowerSpectra
A.Appendices
A.1SomeBasicGlossary
A.2SomeBasicFactsfromLinearAlgebra
A.3SomeElementaryFactsfromODEs
A.4ImplicitFunctionTheorem
A.5SpecialInvariantManifolds
A.6NumericalIntegrationofODEs
A.7SymmetryGroups
A.8NumericalSoftwareandPackages
ListofMajorExamples
References
Index