共查询到18条相似文献,搜索用时 140 毫秒
1.
构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型.每一个种群的成熟期是一个常数,而且只有成年种群存在竞争,幼年的种群并不存在竞争,此外种群个体在空间区域中的运动是随机行走的.我们利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论,证明了连接两个边界平衡解的行波解的存在性. 相似文献
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构造并研究一类具有非局部时滞和非线性种内制约关系的竞争系统的反应扩散模型.利用Wang,Li和Ruan建立的非局部时滞反应扩散方程组波前解存在性的理论,证明了连接两个边界平衡解的行波解的存在性. 相似文献
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谢溪庄 《数学的实践与认识》2013,43(2)
考虑并研究了一类具有分布时滞和非局部空间效应影响的合作系统的反应扩散模型.利用Wang,Li和Ruan建立的非局部时滞反应扩散方程组波前解存在性的理论,证明了连接零平衡解和正平衡解的行波解的存在性. 相似文献
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该文考虑了移动环境下带有非局部扩散项和时滞的反应扩散方程的强迫行波解的存在性和唯一性.首先利用上下解方法和单调迭代原理得到强迫行波解的存在性,其中,该强迫行波解以环境移动的速度来变化.其次,该文结合最大值原理,利用挤压方法得到了该强迫行波解的唯一性.最后,作为该文得到的结论的应用,该文给出了两个经典的模型,一个是带非局部扩散项和时滞的Logistic模型,另一个是带有非局部扩散项和时滞的quasi-Nicholson’s Blowfiles人口模型. 相似文献
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建立并研究了具有营养循环和时滞的浮游动植物模型,模型中描述浮游动植物间的相互作用函数是Holling-Ⅲ型功能反应函数.首先讨论了模型解的正性及有界性,然后分析了系统在无时滞和有时滞两种情况下边界平衡点和正平衡点的局部稳定性,并通过建立适当的Lyapunov函数,讨论了平衡点的全局稳定性.研究表明,随着时滞的增加,系统会出现Hopf分支. 相似文献
7.
对具有扩散项的时滞Mcholson方程的行波解进行了研究.特别是考虑到生物个体在空间位置上的迁移,研究了具有非局部反应的时滞扩散模型.对于弱生成时滞核,运用几何奇异摄动理论,在时滞充分小的情况下,证明了行波解的存在性. 相似文献
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文建立并研究了一个两物种成年个体相互合作的时滞反应扩散模型.利用线性化稳定性方法和Redlinger上、下解方法证明了该模型具有简单的动力学行为,即零平衡点和边界平衡点是不稳定的,而唯一的正平衡点是全局渐近稳定的.同时, 利用Wang, Li 和Ruan建立的具有非局部时滞的反应扩散系统的波前解的存在性,证明了该模型连接零平衡点与唯一正平衡点的波前解的存在性. 相似文献
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构造并研究了一类具有分布时滞和非局部空间效应影响的两种群成年个体相互合作的反应扩散模型.利用线性稳定化方法和Redlinger上下解方法得到了该合作模型的动力性态,并证明了模型在零平衡点和边界平衡点是不稳定的,而在正平衡点是全局渐近稳定的. 相似文献
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Guo Lin 《Journal of Differential Equations》2008,244(3):487-513
A diffusive Lotka-Volterra type model with nonlocal delays for two competitive species is considered. The existence of a traveling wavefront analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a four-dimensional system without delay. Furthermore, in order to prove the asymptotic stability (up to translation) of bistable wavefronts of the system, the existence, regularity and comparison theorem of solutions of the corresponding Cauchy problem are first established for the systems on R by appealing to the theory of abstract functional differential equations. The asymptotic stability (up to translation) of bistable wavefronts are then proved by spectral methods. In particular, we also prove that the spreading speed is unique by upper and lower solutions technique. From the point of view of ecology, our results indicate that the nonlocal delays appeared in the interaction terms are not sensitive to the invasion of species of spatial isolation. 相似文献
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Shuxia Pan Wan-Tong Li Guo Lin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,20(3):377-392
This paper is concerned with the travelling wave fronts of nonlocal reaction-diffusion systems with delays. The existence
of travelling wave fronts for nonlocal reaction-diffusion systems with delays is established by using Schauder’s fixed point
theorem and upper-lower solution technique. Then these results are applied to the nonlocal delayed Logistic model and the
delayed Belousov-Zhabotinskii reaction-diffusion system. Our results show that the time delay can reduce the minimal wave
speed while the nonlocality can increase the minimal wave speed.
Wan-Tong Li: Supported by NNSF of China (10571078) and the Teaching and Research Award Program for Outstanding Young Teachers
in Higher Education Institutions of Ministry of Education of China. 相似文献
13.
This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness. 相似文献
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By considering the random migration of individuals and the period of consuming the captured nutrient, we first introduce the nonlocal delays into a bio-reactor model. The persistence of nontrivial traveling wave solutions then is proved by combining the geometric singular perturbation theory with the center manifold theorem. From the viewpoint of biology, our results indicate that the nonlocality induced by small average delays is harmless to the growth of the species. 相似文献
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Wan-Tong Li Zhi-Cheng Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,20(3):571-591
This paper is concerned with a diffusive and cooperative Lotka–Volterra model with distributed delays and nonlocal spatial
effect. By using an iterative technique recently developed by Wang, Li and Ruan (Traveling wave fronts in reaction-diffusion
systems with spatio-temporal delays, J. Differential Equations
222 (2006), 185–232), sufficient conditions are established for the existence of traveling wave front solutions connecting the
zero and the positive equilibria by choosing different kernels. The result is an extension of an existing result for Fisher-KPP
equation with nonlocal delay and is somewhat parallel to the existing result for diffusive and cooperative Lotka–Volterra
system with discrete delays. 相似文献
16.
This paper is devoted to the study of bistable traveling waves for a competitive–cooperative reaction and diffusion system with nonlocal time delays. The existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite-delay approximations. Then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach. 相似文献
17.
Shangbing Ai 《Journal of Differential Equations》2007,232(1):104-133
We study the existence of traveling wave fronts for a reaction-diffusion equation with spatio-temporal delays and small parameters. The equation reduces to a generalized Fisher equation if small parameters are zero. We present two results. In the first one, we deal with the equation with very general kernels and show the persistence of Fisher wave fronts for all sufficiently small parameters. In the second one, we deal with some particular kernels, with which the nonlocal equation can be reduced to a system of singularly perturbed ODEs, and we are then able to apply the geometric singular perturbation theory and phase plane arguments to this system to show the existence of the minimal wave speed, the existence of a continuum of wave fronts, and the global uniqueness of the physical wave front with each wave speed. 相似文献
18.
In this paper, we consider a Lotka-Volterra competitive system with nonlocal delays and feedback controls. Using the Lyapunov functional and iterative technique method, we investigate the global stability and extinction of the system. Also, we show the influence of feedback controls on dynamic behaviors of the system. Some examples are presented to verify our main results. 相似文献