【作者】 史振霞；

【导师】 李万同；

【作者基本信息】 兰州大学 ， 应用数学， 2008， 硕士

【摘要】 为了更加准确地描述研究对象的时空模式,人们在生物种群、空间生态、流行病学和材料学等领域导出了大量具有空间非局部作用的格微分系统。由于它们涉及空间的非局部作用,因而展现出比经典局部作用更复杂的动力学行为。因此对它们的研究具有重要的理论价值和现实意义。本文研究了二维格上具有年龄结构和固定成熟周期的单种群模型的双稳行波解。该模型反应了空间扩散、非局部时滞及传播方向的共同作用。借助于相应的线性问题,建立了双稳行波解的存在性。通过构造不同的上下解并利用挤压技术得到了双稳行波解的平移唯一性和全局渐近稳定性。与以前的结果相比,本文还考虑了任意传播方向双稳行波解的对称性。这些结果也可以被推广到高维格上。更多还原

【Abstract】 In order to more accurately describe the spatial-temporal patterns of the objects of study, people have derived many lattice differential systems with nonlocal effects in population biology, spatial ecology, materials and disease spread. Because they concern the spatial nonlocal effects, they show a more complex dynamic behavior than the classic. Therefore, research on such issues is of great theoretical value and practical significance.This paper study the bistable traveling waves for a single species model with age structure and a fixed maturation period in a two-dimension lattice. This model reacts the joint effect of the diffusion dynamics, the nonlocal delayed effect and the direction of propagation. With the corresponding linear problem, we obtain the existence of bistable traveling waves. By constructing various pairs of super- and subsolutions and employing the squeezing technique to prove the uniqueness with phase shift and globally exponential stability of bistable traveling waves. Compared with previous results, this paper considers the symmetry of the bistable traveling waves with arbitraryθ. These results can be expended to the case with multi-dimension lattice.更多还原