论文标题
部分可观测时空混沌系统的无模型预测
Steady-state solutions for a reaction-diffusion equation with Robin boundary conditions: Application to the control of dengue vectors
论文作者
论文摘要
在本文中，我们研究了具有罗宾边界条件的有界域中反应扩散方程的初始界价问题，并引入了一些特定参数，以考虑边界上的非零通量。这个问题是在人口替代方法的干预下研究蚊子种群的研究，其中边界条件考虑了个人通过边界的流入和流出。使用相位平面分析，本文根据几个参数研究了非恒定稳态溶液的存在和特性。然后，我们使用线性稳定性的原理来证明其稳定性的足够条件。我们表明，这种控制方法的长期效率在很大程度上取决于处理区的大小和迁移率。为了说明这些理论结果，我们在蚊子人口控制的框架中提供了一些数值模拟。
In this paper, we investigate an initial-boundary-value problem of a reaction-diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary. This problem arises in the study of mosquito populations under the intervention of the population replacement method, where the boundary condition takes into account the inflow and outflow of individuals through the boundary. Using phase-plane analysis, the present paper studies the existence and properties of non-constant steady-state solutions depending on several parameters. Then, we use the principle of linearized stability to prove some sufficient conditions for their stability. We show that the long-time efficiency of this control method depends strongly on the size of the treated zone and the migration rate. To illustrate these theoretical results, we provide some numerical simulations in the framework of mosquito population control.
