共查询到16条相似文献,搜索用时 62 毫秒
1.
2.
研究一类含时滞的Logistic滞反应扩散方程的波前解.通过构造合适的上下解,证明了当时滞充分小时,方程存在波前解.用线性化方法,给出了存在波前解的时滞τ取值范围的一个估计. 相似文献
3.
研究了一类具有分布时滞的扩散种群模型行波解的存在性,证明了当平均时滞充分小时,方程具有连接两个平衡点的单调行波解. 相似文献
4.
5.
利用延拓定理讨论具年龄结构和时滞的自食种群系统正周期解的存在性,得到周期解存在的条件,推广了已有结论. 相似文献
6.
研究了定义在格上并具有时滞的Lotka-Volterra合作系统的波前解.通过构造上下解得到了波前解的存在性,借助于比较原理和渐近传播理论得到了波前解的不存在性,进而在得到了波前解最小波速的充分条件. 相似文献
7.
本文研究了笔者与马知恩教授所提出的一类具有年龄结构的种群发展模型,该模型较完满地解决了古典的Shape-Lotka方程所存在的忽略了孵化期的问题。文中对非线性系统解的适定性、种群发展的有界性和平衡分布作了讨论,利用算子半群理论研究了解的渐近性态,并考虑了一类特殊模型;对结果给予了生物解释。 相似文献
8.
一、引言对于那些模拟、描述生态系统和种群生长规律的数学模型,人们最关心的是正平衡点的存在性、(全局)稳定性、周期解的存在性等问题。然而,有关高维系统,上述问题的研究和讨论是十分困难的。实际上,生态学家不必详尽地了解这些系统复杂而精细的动力学行为(如周期解、混沌现象等),只需知道系统在何种环境或生死条件下能够持续不断地维持下去,即能够持续生存。于是,生态系统的持久性以及与之相关的概念被提出来。持久性问题成为这一领域人们关注和更切合实际的问题。关于离散模型的持久性研究不多,其定义也未给出。本文将给出离散模型持久性的定义,并研究有年龄结构的生长模型 相似文献
9.
具有年龄结构的接种流行病模型正平衡解的全局稳定性 总被引:1,自引:0,他引:1
研究一个具有年龄结构的接种SIS流行病模型正平衡解的稳定性,先利用等价积分方程给出了正平衡解存在的充分条件,再利用迭代方法及函数的单调性,得到了零平衡解与正平衡解全局稳定的充分条件。 相似文献
10.
有史以来,传染病严重危害人类的健康和社会安定,历史证明,传染病的肆虐给人类带来的巨大的痛苦和灾难,虽然人类在治疗传染病方面已经取得了很多有效的成果,但是还面临着传染病所带来的严峻的威胁,我因此们需要对传染病的发病机理、传染规律和治疗方法作进一步研究,本文根据SARS建立了一种新模型,并针对具有年龄结构的SARS传染病模型进行动力学分析。 相似文献
11.
12.
本文讨论了一类造血生物模型在Dirichlet边值条件下稳态解的全局吸引性,并利用上、下解技术和单调迭代方法讨论了行波解的存在性. 相似文献
13.
We develop and investigate a continuum model for invasion of a domain by cells that migrate, proliferate and differentiate.
The model is applicable to neural crest cell invasion in the developing enteric nervous system, but is presented in general
terms and is of broader applicability. Two cell populations are identified and modeled explicitly; a population of precursor
cells that migrate and proliferate, and a population of differentiated cells derived from the precursors which have impaired
migration and proliferation. The equation describing the precursor cells is based on Fisher’s equation with the addition of
a carrying-capacity limited differentiation term. Two variations of the proliferation term are considered and compared. For
most parameter values, the model admits a traveling wave solution for each population, both traveling at the same speed. The
traveling wave solutions are investigated using perturbation analysis, phase plane methods, and numerical techniques. Analytical
and numerical results suggest the existence of two wavespeed selection regimes. Regions of the parameter space are characterized
according to existence, shape, and speed of traveling wave solutions. Our observations may be used in conjunction with experimental
results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, our results
may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells. 相似文献
14.
15.
Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease. 相似文献
16.
本文建立了一类空间非局部带时滞影响的互惠生物种群系统模型.前部分利用线性化方法证明了该模型的简单动力学行为,即证明了零平衡点和两个边界平衡点都是不稳定的,唯一的正平衡点是稳定的,同时还用Redlinger上下解方法得出了该模型的初边值问题存在唯一的正则解;后部分则证明了该反应扩散系统连接零平衡点和正平衡点的行波解的存在性. 相似文献