三维时滞K单调Lotka-Volterra系统的稳定性和行波解的开题报告摘要：本文研究三维时滞K单调Lotka-Volterra系统的稳定性和行波解。首先介绍了Lotka-Volterra系统的基本概念和经典模型，然后引入了时滞和K单调性的概念，构造了三维时滞K单调Lotka-Volterra系统，并分析了其平衡点和稳定性。接着通过分析特征方程的根和Routh-Hurwitz条件，得到了平衡点的稳定性条件，证明了系统的全局渐近稳定性。然后应用行波理论，通过构造合适的伦敦方程和微分方程组，得到了系统的行波解，并分析了其振幅和传播速度。最后通过数值模拟验证了理论结果的正确性。关键词：Lotka-Volterra系统，时滞，K单调性，稳定性，行波解Abstract:Thispaperstudiedthestabilityandtravelingwavesolutionofathree-dimensionaldelayedK-monotoneLotka-Volterrasystem.Firstly,thebasicconceptsandclassicalmodelsofLotka-Volterrasystemwereintroduced.ThentheconceptsofdelayandK-monotonicitywereintroduced,andathree-dimensionaldelayedK-monotoneLotka-Volterrasystemwasconstructedanditsequilibriumpointsandstabilitywereanalyzed.Then,byanalyzingtherootsofthecharacteristicequationandtheRouth-Hurwitzcriterion,thestabilityconditionsoftheequilibriumpointswereobtained,andtheglobalasymptoticstabilityofthesystemwasproved.Then,usingthetravelingwavetheory,byconstructingasuitableLondonequationandasystemofdifferentialequations,thetravelingwavesolutionofthesystemwasobtained,anditsamplitudeandpropagationspeedwereanalyzed.Finally,thecorrectnessofthetheoreticalresultswasverifiedbynumericalsimulation.Keywords:Lotka-Volterrasystem,delay,K-monotonicity,stability,travelingwavesolution.