论文标题
Skorokhod类型的耦合随机系统：数学模型及其应用的适应性
Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications
论文作者
论文摘要
具有复杂生物学相互作用的种群动态，即对不确定性定量的解释，对于许多应用领域至关重要。但是，由于生物系统的复杂性，相应问题的数学公式面临着相应的随机过程在大多数情况下应在有限域中考虑的挑战。我们提出了一个基于一个耦合系统的模型，该模型反映了Skorokhod型随机微分方程，并从边界类似跳跃的出口。该设置描述了主动和被动种群的种群动态。作为主要的工作技术，我们使用紧凑的方法和Skorokhod代表在有限域中提出的SDE的解决方案，以证明系统的适合性。这种功能设置是建模和人口动态模拟领域中的新观点。我们提供模型的细节以及代表性的数值示例，并讨论Wilson-Cowan型系统的应用，对兴奋性和抑制性神经元的两个相互作用种群的动力学进行建模。此外，随机输入电流的存在，反映因子以及泊松跳跃，增加了神经元系统的发射活性。
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains. We propose a model based on a coupled system of reflecting Skorokhod-type stochastic differential equations with jump-like exit from a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use compactness methods and Skorokhod's representation of solutions to SDEs posed in bounded domains to prove the well-posedness of the system. This functional setting is a new point of view in the field of modelling and simulation of population dynamics. We provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson-Cowan-type system, modelling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems.
