科创中国

系统的讨论了具有比率依赖和密度制约的周期捕食-被捕食系统的持久性问题,不仅得到了系统一致持久的充分条件,还得到了必要条件,并且持久性条件在模型中得到验证.

讨论了一类具有非线性密度制约的食饵-捕食者扩散规模型,运用线性化方法和Lyapunov函数法分别讨论该反应扩散模型唯一正平衡点的局部渐近稳定性和全局渐近稳定性.

讨论一类具有性别结构的捕食者-食饵扩散模型在齐次Neumann边界条件下解的存在唯一性和一致有界性,并由线性化方法和Lyapunov函数方法分别证明了该模型正平衡点的局部和全局渐近稳定.

讨论一类扩散的种内相食的捕食者-食饵模型,该模型带有齐次Neumann边界条件.通过迭代的方法证明:在适当的条件下,该模型唯一正常数平衡解全局渐近稳定.

Conservation?of?endangered?sympatric?species?must?be?carefully?executed?to?ensure?that?the?protection?of?one?species?does?not?negatively?impact?the?survival?of?another.?Critically?endangered?Pecos?gambusia?Gambusia?nobilis?and?Leon?Springs?pupfish?Cyprinodon?bovinus,?which?are?endemic?to?a?threatened?desert?spring?habitat,?exemplify?one?such?scenario.?Recently,?this?habitat?has?been?expanded,?and?captively?bred?C.?bovinus?were?released?to?repopulate?an?area?historically?known?to?contain?this?species.?A?previous?study?suggested?that?G.?nobilis?are?detrimental?to?C.?bovinus?populations,?due?to?their?tendency?to?congregate?near?spawning?pairs?and?feed?on?their?eggs.?Whether?G.?nobilis?are?attracted?to?territorial?C.?bovinus,?regardless?of?spawning?behavior,?remains?unclear.?To?determine?this,?the?number?of?G.?nobilis?in?occupied?and?unoccupied?breeding?territories?of?both?wild?and?captively?bred?C.?bovinus?was?measured.?Gambusia?nobilis?densities?were?similar?between?unoccupied?and?occupied?territorial?sites,?suggesting?that?they?do?not?show?a?preference?for?C.?bovinus?territories.?Regardless?of?habitat?location?or?prior?captivity,?territorial?C.?bovinus?significantly?excluded?G.?nobilis?within?their?direct?vicinity?(5?cm),?but?not?from?their?entire?territory.?Decreased?G.?nobilis?density?within?the?habitat?may?allow?C.?bovinus?to?defend?their?breeding?territories?more?readily?during?the?summer?spawning?season.?This?study?provides?empirical?evidence?of?captively?raised?individuals?behaving?similarly?to?wild?indi-?viduals?upon?reintroduction?to?their?natural?habitat?and?support?for?conservation?methods?that?focus?on?common?limiting?factors?between?endangered?species?[Current?Zoology?60?(4):?527-533,?2014].

用定性分析的方法研究了一类具有相互干扰的Leslie捕食与被捕食周期系统的全局性质,讨论了系统的持久性以及周期解的存在唯一性,并且给出了该系统持久性的充分条件以及存在全局渐近稳定正周期解的充分条件.

研究一类具有时滞和阶段结构的捕食模型.分析了正平衡点的稳定性和Hopf分支的存在性.应用中心流形定理和规范型理论,得到了确定Hopf分支方向和分支周期解稳定性的计算公式.

研究了具有时滞的捕食与被捕食系统,分析了系统的正不变集、边界平衡点性质、全局渐近稳定性和持久生存性.当时滞(?)很小时,系统在正平衡点是局部渐近稳定的,当(?)从0增到(?)0时,系统在正平衡点附近产生Hopf分支.

本文研究了具有Gompertz增长率的两种群随机捕食-食饵模型,证明了模型具有全局正解,并对模型的正解进行了有界性估计.

本文研究了一个带有离散和分布时滞的Holling-IV型功能反应的捕食与被捕食模型,将离散时滞r看作分支参数,讨论了正平衡点的局部稳定性和Hopf分支,利用Routh-Hurwitz定理得到了平衡点局部渐近稳定的充分条件.通过分析相应的特征方程,发现随着r穿越某临界值,Hopf分支会发生,并且可能出现小范围周期解.