多区室复杂系统动力学的有效一维降维
Effective one-dimension reduction of multi-compartment complex systems dynamics
AI总结：
提出一种基于量子物理工具的方法，将多维区室复杂系统简化为有效一维表示，以研究平均场动力学、临界行为及随机特征，并在流行病、生态和经济模型中验证了其有效性。
摘要：
一大类系统，包括生态、流行病学和社会学系统，其特征是由被分配到特定类别（例如化学物种、观点或流行病状态）的个体组成的种群，这些类别被建模为区室。由于相互作用和内在动力学，个体可以改变类别，导致浓度随时间变化并表现出复杂行为，这是反应-扩散系统的典型特征。虽然区室建模为研究此类种群的动力学和描述系统的时空演化提供了强大的框架，但它主要依赖于确定性平均场描述来处理具有许多自由度的系统。在这里，我们提出了一种方法，通过利用源自量子物理学的工具，将多维系统系统地简化为有效的一维表示，以缓解区室模型的一些局限性。使用这种简化系统，我们不仅能够研究平均场动力学及其临界行为，还能额外研究捕捉系统基本特征的随机表示。我们通过研究广泛采用的用于研究流行病、生态和经济系统的模型的临界行为，证明了我们形式体系的有效性。
英文摘要：
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are modeled as compartments. Due to interactions and intrinsic dynamics, individuals are allowed to change category, leading to concentrations varying over time with complex behavior, typical of reaction-diffusion systems. While compartmental modeling provides a powerful framework for studying the dynamics of such populations and describe the spatiotemporal evolution of a system, it mostly relies on deterministic mean-field descriptions to deal with systems with many degrees of freedom. Here, we propose a method to alleviate some of the limitations of compartmental models by capitalizing on tools originating from quantum physics to systematically reduce multi-dimensional systems to an effective one-dimensional representation. Using this reduced system, we are able to not only investigate the mean-field dynamics and their critical behavior, but we can additionally study stochastic representations that capture fundamental features of the system. We demonstrate the validity of our formalism by studying the critical behavior of models widely adopted to study epidemic, ecological and economic systems.
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