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Qualitative Analysis and Control of Complex Neural Networks with Delays

Qualitative Analysis and Control of Complex Neural Networks with Delays
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作者: 著 , 著 , 著
出版社: 科学出版社
2015-09
版次: 1
ISBN: 9787030452184
定价: 150.00
装帧: 精装
开本: 16开
纸张: 胶版纸
页数: 388页
正文语种: 英语
分类: 医药卫生
6 张插图图片
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  • 　　Thisbookfocusesonthestabilityofthedynamicalneuralsystem,synchronizationofthecouplingneuralsystemandtheirapplicationsinautomationcontrolandelectricalengineering.Theredefinedconceptofstability,synchronizationandconsensusareadoptedtoprovideabetterexplanationofthecomplexneuralnetwork.Researchersinthefieldsofdynamicalsystems,computerscience,electricalengineeringandmathematicswillbenefitfromthediscussionsoncomplexsystems.Thebookwillalsohelpreaderstobetterunderstandthetheorybehindthecontroltechniqueanditsdesign. 1IntroductiontoNeuralNetworks
    1.1NaturalandArtificialNeuralNetworks
    1.2ModelsofComputation
    1.3NetworksofNeurons
    1.4AssociativeMemoryNetworks
    1.5HopfieldNeuralNetworks
    1.6Cohen-GrossbergNeuralNetworks
    1.7PropertyofNeuralNetwork
    1.8InformationProcessingCapacityofDynamicalSystems
    1.9StabilityofDynamicalNeuralNetworks
    1.10DelayEffectsonDynamicalNeuralNetworks
    1.11FeaturesofLMI-BasedStabilityResults
    1.12Summary
    References

    2PrelinunariesonDynamicalSystemsandStabilityTheory
    2.1OverviewofDynamicalSystems
    2.2DefinitionofDynamicalSystemandItsQualitativeAnalysis
    2.3LyapunovStabilityofDynamicalSystems
    2.4StabilityTheory
    2.5ApplicationsofDynamicalSystemsTheory
    2.6NotationsandDiscussionsonSomeStabilityProblems
    2.6.1NotationsandPreliminaries
    2.6.2DiscussionsonSomeStabilityDefinitions
    2.7Summary
    References

    3SurveyofDynamicsofCohen-Grossberg-TypeRNNs
    3.1Introduction
    3.2MainResearchDirectionsofStabilityofRNNs
    3.2.1DevelopmentofNeuronalActivationFunctions
    3.2.2EvolutionofUncertaintiesinInterconnectionMatrix
    3.2.3EvolutionofTimeDelays
    3.2.4RelationsBetweenEquilibriumandActivationFunctions
    3.2.5DifferentConstructionMethodsofLyapunovFunctions
    3.2.6ExpressionFormsofStabilityCriteria
    3.2.7DomainofAttraction
    3.2.8DifferentKindsofNeuralNetworkModels
    3.3StabilityAnalysisforCohen-Grossberg-TypeRNNs
    3.3.1StabilityonHopfield-TypeRNNs
    3.3.2StabilityonCohen-Grossberg-TypeRNNs
    3.3.3TheCasewithNonnegativeEquilibria
    3.3.4StabilityviaM-MatrixorAlgebraicInequalityMethods
    3.3.5StabilityviaMatrixInequalitiesorMixedMethods
    3.3.6TopicsonRobustStabilityofRNNs
    3.3.7OtherTopicsonStabilityResultsofRNNs
    3.3.8QualitativeEvaluationontheStabilityResultsofRNNs
    3.4NecessaryandSufficientConditionsforRNNs
    3.5Summary
    References

    4Delay-Partitioning-MethodBasedStabilityResultsforRNNs
    4.1Introduction
    4.2ProblemFormulation
    4.3GASCriteriawithSingleWeighting-Delay
    4.3.1Weighting-Delay-IndependentStabilityCriterion
    4.3.2Weighting-Delay-DependentStabilityCriterion
    4.4GASCriteriawithMultipleWeighting-Delays
    4.5ImplementationofOptimalWeighting-DelayParameters
    4.5.1TheSingleWeighting-DelayCase
    4.5.2TheMultipleWeighting-DelaysCase
    4.6IllustrativeExamples
    4.7Summary
    References

    5StabilityCriteriaforRNNsBasedonSecondaryDelayPartitioning
    6LMI-BasedStabilityCriteriaforStaticNeuralNetworks
    7MultipleStabilityforDiscontinuousRNNs
    8LMI-basedPassivityCriteriaforRNNswithDelays
    9DissipativityandInvariantSetsforNeuralNetworkswithDelay
    10SynchronizationStabilityinComplexNeuralNetworks
    11StabilizationofStochasticRNNswithStochasticDelays
    12AdaptiveSynchroruzationofComplexNeuralNetworks
    Index
  • 内容简介:
    　　Thisbookfocusesonthestabilityofthedynamicalneuralsystem,synchronizationofthecouplingneuralsystemandtheirapplicationsinautomationcontrolandelectricalengineering.Theredefinedconceptofstability,synchronizationandconsensusareadoptedtoprovideabetterexplanationofthecomplexneuralnetwork.Researchersinthefieldsofdynamicalsystems,computerscience,electricalengineeringandmathematicswillbenefitfromthediscussionsoncomplexsystems.Thebookwillalsohelpreaderstobetterunderstandthetheorybehindthecontroltechniqueanditsdesign.
  • 目录:
    1IntroductiontoNeuralNetworks
    1.1NaturalandArtificialNeuralNetworks
    1.2ModelsofComputation
    1.3NetworksofNeurons
    1.4AssociativeMemoryNetworks
    1.5HopfieldNeuralNetworks
    1.6Cohen-GrossbergNeuralNetworks
    1.7PropertyofNeuralNetwork
    1.8InformationProcessingCapacityofDynamicalSystems
    1.9StabilityofDynamicalNeuralNetworks
    1.10DelayEffectsonDynamicalNeuralNetworks
    1.11FeaturesofLMI-BasedStabilityResults
    1.12Summary
    References

    2PrelinunariesonDynamicalSystemsandStabilityTheory
    2.1OverviewofDynamicalSystems
    2.2DefinitionofDynamicalSystemandItsQualitativeAnalysis
    2.3LyapunovStabilityofDynamicalSystems
    2.4StabilityTheory
    2.5ApplicationsofDynamicalSystemsTheory
    2.6NotationsandDiscussionsonSomeStabilityProblems
    2.6.1NotationsandPreliminaries
    2.6.2DiscussionsonSomeStabilityDefinitions
    2.7Summary
    References

    3SurveyofDynamicsofCohen-Grossberg-TypeRNNs
    3.1Introduction
    3.2MainResearchDirectionsofStabilityofRNNs
    3.2.1DevelopmentofNeuronalActivationFunctions
    3.2.2EvolutionofUncertaintiesinInterconnectionMatrix
    3.2.3EvolutionofTimeDelays
    3.2.4RelationsBetweenEquilibriumandActivationFunctions
    3.2.5DifferentConstructionMethodsofLyapunovFunctions
    3.2.6ExpressionFormsofStabilityCriteria
    3.2.7DomainofAttraction
    3.2.8DifferentKindsofNeuralNetworkModels
    3.3StabilityAnalysisforCohen-Grossberg-TypeRNNs
    3.3.1StabilityonHopfield-TypeRNNs
    3.3.2StabilityonCohen-Grossberg-TypeRNNs
    3.3.3TheCasewithNonnegativeEquilibria
    3.3.4StabilityviaM-MatrixorAlgebraicInequalityMethods
    3.3.5StabilityviaMatrixInequalitiesorMixedMethods
    3.3.6TopicsonRobustStabilityofRNNs
    3.3.7OtherTopicsonStabilityResultsofRNNs
    3.3.8QualitativeEvaluationontheStabilityResultsofRNNs
    3.4NecessaryandSufficientConditionsforRNNs
    3.5Summary
    References

    4Delay-Partitioning-MethodBasedStabilityResultsforRNNs
    4.1Introduction
    4.2ProblemFormulation
    4.3GASCriteriawithSingleWeighting-Delay
    4.3.1Weighting-Delay-IndependentStabilityCriterion
    4.3.2Weighting-Delay-DependentStabilityCriterion
    4.4GASCriteriawithMultipleWeighting-Delays
    4.5ImplementationofOptimalWeighting-DelayParameters
    4.5.1TheSingleWeighting-DelayCase
    4.5.2TheMultipleWeighting-DelaysCase
    4.6IllustrativeExamples
    4.7Summary
    References

    5StabilityCriteriaforRNNsBasedonSecondaryDelayPartitioning
    6LMI-BasedStabilityCriteriaforStaticNeuralNetworks
    7MultipleStabilityforDiscontinuousRNNs
    8LMI-basedPassivityCriteriaforRNNswithDelays
    9DissipativityandInvariantSetsforNeuralNetworkswithDelay
    10SynchronizationStabilityinComplexNeuralNetworks
    11StabilizationofStochasticRNNswithStochasticDelays
    12AdaptiveSynchroruzationofComplexNeuralNetworks
    Index
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