生物数学影印版（第2版）

1.ContinuousPopulationModelsforSingleSpecies
1.1ContinuousGrowthModels
1.2InsectOutbreakModel:SpruceBudworm
1.3DelayModels
1.4LinearAnalysisofDelayPopulationModels:PeriodicSolutions
1.5DelayModelsinPhysiology:DynamicDiseases
1.6HarvestingaSingleNaturalPopulation
*1.7PopulationModelwithAgeDistribution
Exercises
2.DiscretePopulationModelsforaSingleSpecies
2.1Introduction:SimpleModels
2.2Cobwebbing:AGraphicalProcedureofSolution
2.3DiscreteLogisticModel:Chaos
2.4Stability,PeriodicSolutionsandBifurcations
2.5DiscreteDelayModels
2.6FisheryManagementModel
2.7EcologicalImplicationsandCaveats
Exercises
3.ContinuousModelsforInteractingPopulations
3.1Predator-PreyModels:Lotka-VolterraSystems
3.2ComplexityandStability
3.3RealisticPredator-PreyModels
3.4AnalysisofaPredator-PreyModelwithLimitCyclePeriodic
Behaviour:ParameterDomainsofStability
3.5CompetitionModels:PrincipleofCompetitiveExclusion
3.6MutualismorSymbiosis
3.7GeneralModelsandSomeGeneralandCautionaryRemarks
3.8ThresholdPhenomena
Exercises
4.DiscreteGrowthModelsforInteractingPopulations
4.1Predator-PreyModels:DetailedAnalysis
*4.2SynchronizedInsectEmergence:13YearLocusts
4.3BiologicalPestControl:GeneralRemarks
Exercises
5.ReactionKinetics
5.1EnzymeKinetics:BasicEnzymeReaction
5.2Michaelis-MentenTheory:DetailedAnalysisandthe
Pseudo-SteadyStateHypothesis
5.3CooperativePhenomena
5.4Autocatalysis,ActivationandInhibition
5.5MultipleSteadyStates,MushroomsandIsolas
Exercises
6.BiologicalOscillatorsandSwitches
6.1Motivation,HistoryandBackground
6.2FeedbackControlMechanisms
6.3OscillationsandSwitchesInvolvingTwoorMoreSpecies:
GeneralQualitativeResults
6.4SimpleTwo-SpeciesOscillators:ParameterDomain
DeterminationforOscillations
6.5Hodgkin-HuxleyTheoryofNerveMembranes:
FitzHugh-NagumoModel
6.6ModellingtheControlofTestosteroneSecretion
Exercises
7.Belousov-ZhabotinskiiReaction
7.1BelousovReactionandtheField-Noyes(FN)Model
7.2LinearStabilityAnalysisoftheFNModelandExistence
ofLimitCycleSolutions
7.3Non-localStabilityoftheFNModel
7.4RelaxationOscillators:Approximationforthe
Belousov-ZhabotinskiiReaction
7.5AnalysisofaRelaxationModelforLimitCycleOscillations
intheBelousov-ZhabotinskiiReaction
Exercises
8.PerturbedandCoupledOscillatorsandBlackHoles
8.1PhaseResettinginOscillators
8.2PhaseResettingCurves
8.3BlackHoles
8.4BlackHolesinRealBiologicalOscillators
8.5CoupledOscillators:MotivationandModelSystem
*8.6SingularPerturbationAnalysis:PreliminaryTransformation
*8.7SingularPerturbationAnalysis:TransformedSystem
*8.8SingularperturbationAnalysis:Two-TimeExpansion
*8.9AnalysisofthePhaseShiftEquationandApplication
toCoupledBelousov-ZhabotinskiiReactions
Exercises
9.ReactionDiffusion,ChemotaxisandNon-localMechanisms
9.1SimpleRandomWalkDerivationoftheDiffusionEquation
9.2ReactionDiffusionEquations
9.3ModelsforInsectDispersal
9.4Chemotaxis
*9.5Non-localEffectsandLongRangeDiffusion
*9.6CellPotentialandEnergyApproachtoDiffusion
Exercises
10.OscillatorGeneratedWavePhenomenaandCentralPattern
Generators
10.1KinematicWavesintheBelousov-ZhabotinskiiReaction
10.2CentralPatternGenerator:ExperimentalFactsinthe
SwimmingofFish
*10.3MathematicalModelfortheCentralPatternGenerator
*10.4AnalysisofthePhase-CoupledModelSystem
Exercises
11.BiologicalWaves:SingleSpeciesModels
11.1BackgroundandtheTravellingWaveForm
11.2FisherEquationandPropagatingWaveSolutions
11.3AsymptoticSolutionandStabilityofWavefrontSolutions
oftheFisherEquation
11.4Density-DependentDiffusionReactionDiffusionModels
andSomeExactSolutions
11.5WavesinModelswithMulti-SteadyStateKinetics:
TheSpreadandControlofanInsectPopulation
11.6CalciumWavesonAmphibianEggs:ActivationWaves
onMedakaEggs
Exercises
12.BiologicalWaves:Multi-speciesReactionDiffusionModels
12.1IntuitiveExpectations
12.2WavesofPursuitandEvasioninPredator-PreySystems
12.3TravellingFrontsintheBelousov-ZhabotinskiiReaction
12.4WavesinExcitableMedia
12.5TravellingWaveTrainsinReactionDiffusionSystems
withOscillatoryKinetics
*12.6LinearStabilityofWaveTrainSolutionsof-Systems
12.7SpiralWaves
*12.8SpiralWaveSolutionsof-ReactionDiffusionSystems
Exercises
*13.TravellingWavesinReactionDiffusionSystemswith
WeakDiffusion:AnalyticalTechniquesandResults
*13.1ReactionDiffusionSystemwithLimitCycleKineticsand
WeakDiffusion:ModelandTransformedSystem
*13.2SingularPerturbationAnalysis:ThePhaseSatisfies
Burgers'Equation
*13.3TravellingWavetrainSolutionsforReactionDiffusionSystems
withLimitCycleKineticsandWeakDiffusion:Comparison
withExperiment
14.SpatialPatternFormationwithReaction/PopulationInteraction
DiffusionMechanisms
14.1RoleofPatterninDevelopmentalBiology
14.2ReactionDiffusion(Turing)Mechanisms
14.3LinearStabilityAnalysisandEvolutionofSpatialPattern:
GeneralConditionsforDiffusion-DrivenInstability
14.4DetailedAnalysisofPatternInitiationinaReactionDiffusion
Mechanism
14.5DispersionRelation,TuringSpace,ScaleandGeometryEffects
inPatternFormationinMorphogeneticModels
14.6ModeSelectionandtheDispersionRelation
14.7PatternGenerationwithSingleSpeciesModels:
SpatialHeterogeneitywiththeSpruceBudwormModel
14.8SpatialPatternsinScalarPopulationInteraction-Reaction
DiffusionEquationswithConvection:EcologicalControl
Strategies
*14.9NonexistenceofSpatialPatternsinReactionDiffusion
Systems:GeneralandParticularResults
Exercises
15.AnimalCoatPatternsandOtherPracticalApplications
ofReactionDiffusionMechanisms
15.1MammalianCoatPatterns-'HowtheLeopardGotItsSpots'
15.2APatternFormationMechanismforButterflyWingPatterns
15.3ModellingHairPatternsinaWhorlinAcetabularia
16.NeuralModelsofPatternFormation
16.1SpatialPatterninginNeuralFiringwithaSimple
Activation-InhibitionModel
16.2AMechanismforStripeFormationintheVisualCortex
16.3AModelfortheBrainMechanismUnderlyingVisual
HallucinationPatterns
16.4NeuralActivityModelforShellPatterns
Exercises
17.MechanicalModelsforGeneratingPatternandForm
inDevelopment
17.1IntroductionandBackgroundBiology
17.2MechanicalModelforMesenchymalMorphogenesis
17.3LinearAnalysis,DispersionRelationandPatternFormation
Potential
17.4SimpleMechanicalModelsWhichGenerateSpatialPatterns
withComplexDispersionRelations
17.5PeriodicPatternsofFeatherGerms
17.6CartilageCondensationsinLimbMorphogenesis
17.7MechanochemicalModelfortheEpidermis
17.8TravellingWaveSolutionsoftheCytogelModel
17.9FormationofMicrovilli
17.10OtherApplicationsofMechanochemicalModels
Exercises
18.EvolutionandDevelopmentalProgrammes
18.1EvolutionandMorphogenesis
18.2EvolutionandMorphogeneticRulesinCartilageFormation
intheVertebrateLimb
18.3DevelopmentalConstraints,MorphogeneticRulesand
theConsequencesforEvolution
19.EpidemicModelsandtheDynamicsofInfectiousDiseases
19.1SimpleEpidemicModelsandPracticalApplications
19.2ModellingVenerealDiseases
19.3Multi-groupModelforGonorrheaandItsControl
19.4AIDS:ModellingtheTransmissionDynamicsoftheHuman
ImmunodeficiencyVirus(HIV)
19.5ModellingthePopulationDynamicsofAcquiredImmunity
toParasiteInfection
*19.6AgeDependentEpidemicModelandThresholdCriterion
19.7SimpleDrugUseEpidemicModelandThresholdAnalysis
Exercises
20.GeographicSpreadofEpidemics
20.1SimpleModelfortheSpatialSpreadofanEpidemic
20.2SpreadoftheBlackDeathinEurope1347-1350
20.3TheSpatialSpreadofRabiesAmongFoxesI:Background
andSimpleModel
20.4TheSpatialSpreadofRabiesAmongFoxesII:ThreeSpecies
(SIR)Model
20.5ControlStrategyBasedonWavePropagationintoa
Non-epidemicRegion:EstimateofWidthofaRabiesBarrier
20.6Two-DimensionalEpizooticFrontsandEffectsofVariable
FoxDensities:QuantitativePredictionsforaRabiesOutbreak
inEngland
Exercises
Appendices
1.PhasePlaneAnalysis
2.Routh-HurwitzConditions,JuryConditions,Descartes'Rule
ofSignsandExactSolutionsofaCubic
3.HopfBifurcationTheoremandLimitCycles
4.GeneralResultsfortheLaplacianOperatorinBounded
Domains
Bibliography
Index