共查询到17条相似文献,搜索用时 78 毫秒
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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
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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
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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
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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
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一类带时滞竞争模型的周期解 总被引:2,自引:0,他引:2
研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统.用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件. 相似文献
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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
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运用Leray-Schauder不动点定理研究具有无穷时滞的泛函微分方程的正周期解的存在性问题,获得了存在正周期解的充分条件,改进了文献[3]中的结果. 相似文献
11.
Traveling waves of calcium are widely observed under the condition that the free cytosolic calcium is buffered. Thus it is
of physiological interest to determine how buffers affect the properties of calcium waves. Here we summarise and extend previous
results on the existence, uniqueness and stability of traveling wave solutions of the buffered bistable equation, which is
the simplest possible model of the upstroke of a calcium wave. Taken together, the results show that immobile buffers do not
change the existence, uniqueness or stability of the traveling wave, while mobile buffers can eliminate a traveling wave.
However, if a wave exists in the latter case, it remains unique and stable.
相似文献
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We establish the existence of traveling wave solutions for a nonlinear partial differential equation that models a logistically
growing population whose movement is governed by an advective process. Conditions are presented for which traveling wave solutions
exist and for which they are stable to small semi-finite domain perturbations. The wave is of mathematical interest because
its behavior is determined by a singular differential equation and those with small speed of propagation steepen into a shock-like
solutions. Finally, we indicate that the smoothing presence of diffusion allows wave persistence when an advective slow moving
wave may collapse.
Received: 24 November 1997 / Revised version: 13 July 1998 相似文献
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Propagation of HBV with spatial dependence 总被引:1,自引:0,他引:1
A mathematical model is proposed to simulate the hepatitis B virus (HBV) infection with spatial dependence. The existence of traveling waves is established via the geometric singular perturbation method. Numerical simulations show that the model admits non-monotone traveling profiles. Influences of various parameters on the minimum wave speed are also discussed. 相似文献
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Li B 《Journal of mathematical biology》2012,65(5):855-873
We propose an integro-difference equation model to predict the spatial spread of a plant population with a seed bank. The formulation of the model consists of a nonmonotone convolution integral operator describing the recruitment and seed dispersal and a linear contraction operator addressing the effect of the seed bank. The recursion operator of the model is noncompact, which poses a challenge to establishing the existence of traveling wave solutions. We show that the model has a spreading speed, and prove that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions by using an asymptotic fixed point theorem. Our numerical simulations show that the seed bank has the stabilizing effect on the spatial patterns of traveling wave solutions. 相似文献
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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
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This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe
the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when
the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species
while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition
disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual
population densities at the coexistence domain are lower than the case when the competition vanishes. 相似文献