一类具AIlee效应的两阶段种群扩散模型动力学

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关键词：Allee效应；蓝蟹模型；扩散；阶段结构；全局稳定性

DOI：10. 15938/j. jhust. 2025.05.014

中图分类号：0175.2 文献标志码：A 文章编号：1007-2683（2025）05-0135-10

Abstract：Thedynamicsofa class of thebluecrabpopulation modelwithtwo-stageandAleeefectwithhomogeneous Neumann boundarycondionsisstudiedThebasicpropertiesofthesolution，thelocalandglobalstabilityoftheequilibria，thenon-existencef non-constantteady-statesolutions，andtheexistenceof thefishingthresholdareotainedintheabsenceandpreseneofdifusion， respectively，byapplyingthecentralmanifoldtheorem，thenormalformtheory，ndconstructingLyapunovfunctions.Whenthefishing rateislargerthanthethreshold，thebluecabpopulationgoesextincteventually.Whenthefishingrateislessthanorequaltothe threshold，Alleeectocus，andteextintionofbuecabopulationdependsonteinitialvue.Finalltetheoreticalsuls are verified by numerical simulations.

Keywords：Allee effect； blue crabs model； diffusion；stage-structure； global stability

0 引言

蓝蟹又名青蟹、美味优游蟹，生存在大西洋西岸和墨西哥湾沿岸海洋，具有非常重要的商业价值和渔业价值[1-4]。（剩余10037字）