论文标题
在离散时间离散空间人口模型中锁定前线
Locked fronts in a discrete time discrete space population model
论文作者
论文摘要
在空间栖息地为晶格的情况下，人们考虑了人口增长和扩散的模型，并在生成上发生繁殖。所得的离散动力系统表现出速度锁定，其中观察到合理的速度侵袭前线会随着参数的变化而持续存在。在本文中，我们为特定的分段线性再现函数构建了锁定前部。这些方面被证明是对不稳定状态附近线性系统呈指数衰减溶液的线性组合。然后，基于这些前解决方案，我们得出参数空间中锁定区域边界的表达式。由于迁移参数趋于零，因此我们在极限的锁定区域中获得了领先的订单扩展。还建立了指数加权空间的严格频谱稳定性。
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts are observed to persist as parameters are varied. In this article, we construct locked fronts for a particular piecewise linear reproduction function. These fronts are shown to be linear combinations of exponentially decaying solutions to the linear system near the unstable state. Based upon these front solutions, we then derive expressions for the boundary of locking regions in parameter space. We obtain leading order expansions for the locking regions in the limit as the migration parameter tends to zero. Strict spectral stability in exponentially weighted spaces is also established.
