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捕食者-食饵系统的行波解与渐近传播
Project Number11461040
潘书霞
Abstract捕食者-食饵系统是描述自然现象的重要模型,与竞争系统、合作系统相比较,此类系统因单调性条件特殊使得相关研究有其自身的复杂之处,许多重要模型的空间传播性质还未被研究,对一些系统的探讨主要集中在行波解存在性因而时空传播阈值理论也不够完善。本项目以建立两种群及多种群系统行波解的最小波速、对捕食者和食饵的渐近传播速度进行估计为具体目标。在行波解研究中,将使用广义上下解解决存在性。对于渐近行为以及最小波速,将在使用比较原理的基础上,结合动力系统理论及经典渐近传播理论进行研究。在渐近传播研究中,将结合算子半群理论、捕食者-食饵系统的比较原理、非自治方程的传播理论、经典渐近传播理论对于不同未知函数进行估计,并着力体现其中非线性项的非平凡作用。在本项目中,对多种群耦合系统时空传播阈值理论的研究以及要体现的非线性项复杂性是项目的特色。【英文摘要】Inappliedmathematics,predator-preysystemsareveryimportanttomodeltheenerytransmission,andtheyadmitmorecomplexdynamicalbehaviorthanthecompetitiveandcooperativesystems.Inparticular,thespecialmonotoneconditionsofpredator-preysystemsleadtomuchdifficultyinformulatingthespatialpropagationofthem.Thegoalofthisproposalistoinvestigatethespatialpropagationofpredator-preysystemsbycombiningthetheoryofpartialdifferentialequationswiththemethodofmonotonedynamicalsystems.Wewillestablishtheminimalwavespeedoftravelingwavesolutionsandestimatetheasymptoticspeedofspreadingofpredator-preysystemswithtwoormultispecies.Toobtaintheexistenceoftravelingwavesolutions,thegeneralizedupperandlowersolutionswillbeutilized.Inthestudyofasymptoticbehaviorandminimalwavespeedoftravelingwavesolutions,wewillapplythemethodofmonotonedynamicalsystemsandtheclassicaltheoryofasymptoticspreadingofKPPequation.Theasymptoticspreadingwillbeinvestigatedbythetheoryofsemigroupsoflinearoperators,comparisonprincipleappealingtothepredator-preysystemsandtheasymptoticspreadingofnonautonomousequations.Theproposedworkwillleadtoabetterunderstandingofthedynamicalbehaviorofpredator-preysystemsfromtheviewpointofspatialpropagation,especiallytothedynamicsofmultispeciesmodlesandtheroleofcouplednonlinearities.
Subtype地区科学基金项目
Project Source国家自然科学基金
2015-01
End Date2018-12
MOST Discipline Catalogue01 - 数学 ; 0108 - 偏微分方程
Host Institution兰州理工大学
Project Funding360000.0
CountryCN
Language中文
Document Type项目
Identifierhttp://ir.lut.edu.cn/handle/2XXMBERH/64740
Collection理学院
Recommended Citation
GB/T 7714
潘书霞.捕食者-食饵系统的行波解与渐近传播.2015.
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