共查询到19条相似文献,搜索用时 297 毫秒
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一类带Beddington-DeAngelis反应项的捕食模型平衡态的分歧解 总被引:1,自引:0,他引:1
本文利用极值原理,L-S度理论,特征值扰动理论及分歧理论,主要研究了一类带Beddington-DeAngelis反应项的捕食模型在Dirichlet边界条件下的平衡态局部分歧解与全局分歧解,给出了局部分歧解存在的充分条件和稳定性,并且得到其平衡态全局分歧解及其走向。 相似文献
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本文讨论了在无界区域中,带有Dirichlet边界条件的一类多分子反应模型。利用Liapunov-schmidt约化方法,我们证明了关于x为2π/k1周期的定态分歧解的存在性。 相似文献
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本文利用局部分歧理论和局部稳定性理论,讨论了一类具有避难所的两物种间的捕食-食饵模型在非齐次Dirichlet边界条件下分歧解的性质,其功能反应函数为Holling Ⅱ型.利用局部分歧和局部稳定性理论给出了分歧解局部稳定的条件;同时利用度理论得到了局部分歧可以延拓到整体分歧的结论. 相似文献
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研究了一类带Ivlev型反应函数的非均匀恒化器竞争模型的全局分歧.利用最大值原理获得了共存解的先验估计,借助于特征值理论、上下解方法得到了共存解存在的必要条件,采用局部分歧理论构造了共存解的局部分支,并运用全局分歧理论证明了共存解的局部分支可延拓为全局分支.结果表明该全局分支连接了模型的两半平凡解分支.从生物学角度看,当两竞争物种的最大生长率满足一定条件时,两物种可以共存. 相似文献
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本文讨论一类具有B-D反应函数和Allee效应的捕食-食饵扩散模型正解的存在性、唯一性和多重性.首先运用不动点指数理论得到了正解存在的充分条件.接着利用特征值的变分原理给出了正解的唯一性条件.最后通过分析极限系统的正解,运用不动点指数理论、分歧理论和扰动理论确定了正解的确切重数和稳定性.讨论结果表明:只要Allee效应... 相似文献
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本文在齐次Neumann边界条件下研究了一类捕食-食饵模型正平衡解的稳定性与存在性.首先,我们利用算子谱理论得到了正常数平衡解的一致渐近稳定性,其次,运用最大值原理和Harnack不等式,我们给出了正平衡解的先验估计,再次,利用积分的性质并结合ε-Young不等式和Poincar′e不等式,文中证明了非常数正平衡解的不存在性,最后,利用Leray-Schauder度理论证明了非常数正平衡解的存在性,并且给出了正平衡解存在的充分条件.研究结果表明,当参数满足一定条件时,两物种可以共存. 相似文献
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Study on cavitated bifurcation problems for spheres composed of hyper-elastic materials 总被引:1,自引:0,他引:1
In this paper, spherical cavitated bifurcation problems are examined for incompressible hyper-elastic materials and compressible
hyper-elastic materials, respectively. For incompressible hyper-elastic materials, a cavitated bifurcation equation that describes
cavity formation and growth for a solid sphere, composed of a class of transversely isotropic incompressible hyper-elastic
materials, is obtained. Some qualitative properties of the solutions of the cavitated bifurcation equation are discussed in
the different regions of the plane partitioned by material parameters indicating the degree of radial anisotropy in detail.
It is shown that the cavitated bifurcation equation is equivalent, by use of singularity theory, to a class of normal forms
with single-sided constraint conditions at the critical point. Stability and catastrophe of the solutions of the cavitated
bifurcation equation are discussed by using the minimal potential-energy principle. For compressible hyper-elastic materials,
a group of parameter-type solutions for the cavitated deformation for a solid sphere, composed of a class of isotropic compressible
hyper-elastic materials, is obtained. Stability of the solutions is also discussed. 相似文献
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Summary The linear and non-linear stability of double diffusive convection in a sparsely packed porous layer is studied using the Brinkman model. In the case of linear theory conditions for both simple and Hopf bifurcations are obtained. It is found that Hopf bifurcation always occurs at a lower value of the Rayleigh number than one obtained for simple bifurcation and noted that an increase in the value of viscosity ratio is to delay the onset of convection. Non-linear theory is studied in terms of a simplified model, which is exact to second order in the amplitude of the motion, and also using modified perturbation theory with the help of self-adjoint operator technique. It is observed that steady solutions may be either subcritical or supercritical depending on the choice of physical parameters. Nusselt numbers are calculated for various values of physical parameters and representative streamlines, isotherms and isohalines are presented. 相似文献
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本文通过建立两个动力学模型,研究了HIV感染者中癌症的高发现象。我们分别研究了其平衡态的存在性及稳定性。对正平衡态还发现了Hopf分支的存在,并发现随着分支参数的变化,系统出现了周期解与混沌交替出现的现象。 相似文献
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本文研究一类具有时滞和阶段结构的生态-流行病模型的稳定性及其Hopf分支.给出了边界平衡点和正平衡点存在的充分条件;通过分析特征方程,运用Hurwitz判定定理,讨论了边界平衡点和正平衡点的局部稳定性,并得到了正平衡点附近存在Hopf分支的充分条件;通过构造适当的Lyapunov泛函,运用LaSall不变集原理,讨论了边界平衡点和正平衡点的全局稳定性,从而得到了该生态模型永久持续生存与灭绝的充分条件. 相似文献