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非拟单调时滞反应扩散方程单稳行波解的稳定性 Title:StabilityAnalysisofNon-monotonicTime-delayedReaction-DiffusionEquationwithSingleSteady-stateWaveSolution Abstract: Reaction-diffusionequationsarewidelyusedinmanyfieldstodescribethedynamicsofcomplexsystems.Inthispaper,weinvestigatethestabilityanalysisofthenon-monotonictime-delayedreaction-diffusionequationwithasinglesteady-statewavesolution.Thenon-monotonictimedelayintheequationintroducesanadditionalchallengetothestabilityanalysis.Wefirstderivethenon-monotonictime-delayedreaction-diffusionequationandthenanalyzethestabilityofthesinglesteady-statewavesolutionusingvariousmathematicaltechniques,includinglinearstabilityanalysis,spectralanalysis,andnumericalsimulations.Ourresultscontributetoabetterunderstandingofthecomplexdynamicsandstabilitypropertiesofnon-monotonictime-delayedreaction-diffusionsystems. 1.Introduction 1.1BackgroundandMotivation 1.2ObjectivesoftheStudy 2.MathematicalFormulation 2.1Non-monotonicTime-delayedReaction-DiffusionEquation 2.2SingleSteady-stateWaveSolution 3.LinearStabilityAnalysis 3.1LinearizationoftheNon-monotonicTime-delayedReaction-DiffusionEquation 3.2StabilityConditions 3.3AnalysisofStabilityBoundaries 4.SpectralAnalysis 4.1IntroductiontoSpectralAnalysis 4.2SpectralPropertiesofNon-monotonicTime-delayedReaction-DiffusionEquation 4.3StabilityAnalysisUsingSpectralTechniques 5.NumericalSimulations 5.1NumericalSchemeforSolvingNon-monotonicTime-delayedReaction-DiffusionEquation 5.2StabilityAnalysisUsingNumericalSimulations 5.3ComparisonwithAnalyticalResults 6.Discussion 6.1InterpretationofStabilityAnalysisResults 6.2ImplicationsforReal-worldSystems 6.3LimitationsandFutureDirections 7.Conclusion 7.1SummaryofFindings 7.2SignificanceoftheStudy 7.3FutureResearchDirections References Inthispaper,webeginbyprovidingthenecessarybackgroundandmotivationforstudyingnon-monotonictime-delayedreaction-diffusionequations.Wethenintroducethemathematicalformulationofthenon-monotonictime-delayedreaction-diffusionequation,highlightingtheuni