论文标题
一种使用两个生理结构的线性种群模型稳定性的伪光谱方法
A pseudospectral method for investigating the stability of linear population models with two physiological structures
论文作者
论文摘要
线性群体模型的无效模型的渐近稳定性，其两个生理结构以一阶双曲PDE配方，由其无限发电机的光谱确定。我们在Carathéodory的意义上提出了完全连续函数空间中问题的等效重新重新制定，以便相应的无限发生器的域是由微不足道的边界条件定义的。通过双变量搭配，我们将重新计算的运算符离散为有限维矩阵，可用于近似原始的无穷小发电机的光谱。最后，我们提供了测试示例，说明了近似特征值和特征功能的融合行为及其对模型系数规则性的依赖性。
The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. We propose an equivalent reformulation of the problem in the space of absolutely continuous functions in the sense of Carathéodory, so that the domain of the corresponding infinitesimal generator is defined by trivial boundary conditions. Via bivariate collocation, we discretize the reformulated operator as a finite-dimensional matrix, which can be used to approximate the spectrum of the original infinitesimal generator. Finally, we provide test examples illustrating the converging behavior of the approximated eigenvalues and eigenfunctions, and its dependence on the regularity of the model coefficients.
