静态与时间多重网络上Turing不稳定性检测的理论

中文摘要 AI 辅助

本研究旨在引入并讨论一种用于多重网络线性不稳定性分析的通用框架，该框架适用于层间扩散缺失的情况，其特定动机是检测Turing不稳定性。该形式体系针对m个未知量进行了全面阐述，每个未知量均作为非自治反应扩散方程的解，定义在含n个节点的时间多重网络上。此外，我们识别出一类拉普拉斯矩阵可交换的多重网络，在此类网络中可取得分析进展，并推导了控制不稳定性的显式不等式。为探究该形式体系，我们将其应用于群岛上的两物种捕食-食饵模型这一具体实例，其中节点被解释为岛屿，边对应各物种的运输网络，且非自治设置用于模拟多种自然现象。

英文摘要

The purpose of this work is to introduce and discuss a general framework for performing a linear instability analysis on multiplex networks, in the absence of inter-layer diffusion, with the specific motivation of detecting the Turing instability. The formalism itself is presented in full generality for $m$-unknowns, each of which arise as solutions of non-autonomous reaction-diffusion equations, on $n$-node temporal multiplex networks. In addition, we identify a class of multiplex networks for which the Laplacian matrices commute. In this setting analytical progress can be made and the explicit inequalities, governing instability, are derived. In order to explore our formalism we apply it to the specific example of a two-species predator-prey model on archipelagos. Here nodes are interpreted as islands and edges correspond to the transportation network for each species. Moreover, the non-autonomous setting is used to model a variety of natural phenomena.

发表机构

• Department of Mathematics and Statistics, University of Otago（奥塔哥大学数学与统计系）

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