A numerical approach for investigating the stability of equilibria for structured population models.
A numerical approach for investigating the stability of equilibria for structured population models.
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DOI：
10.1080/17513758.2013.789562
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发表时间：
2013
影响因子：
2.8
通讯作者：
Vermiglio R
中科院分区：
文献类型：
--
作者：
Breda D;Diekmann O;Maset S;Vermiglio R
我们感兴趣的是在系统的沃尔泰拉功能方程耦合延迟微分方程建模的结构种群平衡的渐近稳定性。基于研究线性化系统的特征方程的标准方法往往是复杂的，甚至是无法实现的。因此，我们提出并研究了一种数值方法来计算相关的无穷小生成元的特征值。后者是通过使用伪谱的方法离散化，和由此产生的矩阵的特征值是寻求近似。提出了一种从模型系数和参数显式构造矩阵的算法。该方法首先在学术实例上进行测试，表明它也适用于一类比上面提到的大得多的数学模型，包括中性和混合型方程。然后，为了说明所提出的技术，特别是研究分叉的有效性，提供了同类相食和消费者资源模型的应用程序。AMS科目分类：34 L16; 37 M20; 65 L07; 92 D25
We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems of Volterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved or even unattainable. Therefore, we propose and investigate a numerical method to compute the eigenvalues of the associated infinitesimal generator. The latter is discretized by using a pseudospectral approach, and the eigenvalues of the resulting matrix are the sought approximations. An algorithm is presented to explicitly construct the matrix from the model coefficients and parameters. The method is tested first on academic examples, showing its suitability also for a class of mathematical models much larger than that mentioned above, including neutral- and mixed-type equations. Applications to cannibalism and consumer–resource models are then provided in order to illustrate the efficacy of the proposed technique, especially for studying bifurcations. AMS Subject Classifications: 34L16; 37M20; 65L07; 92D25
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