论文标题
在不对称相互作用的数学模型中，指数分化解决方案的同步和稳定性分析
Synchronization and stability analysis of an exponentially diverging solution in a mathematical model of asymmetrically interacting agents
论文作者
论文摘要
这项研究涉及现有的非对称相互作用剂的数学模型。我们分析了该模型的以下两个先前未关注的特征：（i）增长率的同步和（ii）阻尼振荡的初始值依赖性。通过应用可变变换和时间尺度分离的技术，我们对解决方案进行了稳定分析。我们发现（i）所有增长率同步到与最小生长速率相同的值，并且（ii）如果最慢的生长剂的初始值足够小，则会出现振荡动力学。此外，我们的分析方法提出了一种将稳定性分析应用于指数分化的解决方案的方法，我们认为这也是本研究的贡献。尽管最初提出了采用的模型作为传染病模型，但我们不讨论其生物学相关性，而只是关注技术方面。
This study deals with an existing mathematical model of asymmetrically interacting agents. We analyze the following two previously unfocused features of the model: (i) synchronization of growth rates and (ii) initial value dependence of damped oscillation. By applying the techniques of variable transformation and time-scale separation, we perform the stability analysis of a diverging solution. We find that (i) all growth rates synchronize to the same value that is as small as the smallest growth rate and (ii) oscillatory dynamics appear if the initial value of the slowest-growing agent is sufficiently small. Furthermore, our analytical method proposes a way to apply stability analysis to an exponentially diverging solution, which we believe is also a contribution of this study. Although the employed model is originally proposed as a model of infectious disease, we do not discuss its biological relevance but merely focus on the technical aspects.
