AI 中文总结
研究受异质主体成本约束的逻辑动力学，从SDE和FPE两个观点分析其适定性，通过在成本约束中添加正则化因子防止数值计算崩溃，给出计算FPE的数值方法并进行交叉领域示范应用研究。
AI 中文摘要
本文构建了受异质主体约束的逻辑动力学，这是一个非线性动力系统。从基于主体（随机微分方程：SDE）和概率（福克 - 普朗克方程：FPE）两个观点研究其适定性。主体行动的状态空间是有限维欧几里得空间中的紧域。SDE是麦克凯恩 - 弗拉索夫型且由有限变差跳跃驱动，FPE是一个非线性积分 - 微分方程。对FPE数学分析的关键是在成本约束中添加正则化因子以减轻逻辑函数的爆炸。此性质也适用于麦克凯恩 - 弗拉索夫SDE。还给出基于朴素有限差分离散化计算FPE的数值方法及示例，表明正则化方法在防止数值计算崩溃时对数值解影响不大。最后进行了环境、能源和渔业资源交叉的示范应用研究。
英文摘要
The logit dynamic, a nonlinear dynamical system, subject to a const constraint with heterogeneous agents is formulated, and its well-posedness is studied from both agent-based (stochastic differential equation: SDE) and probabilistic (Fokker-Planck equation: FPE) viewpoints. The state space of agent actions is a compact domain in a finite-dimensional Euclidean space. The SDE is of the McKean-Vlasov type and is driven by jumps with finite variations, whereas the FPE is a nonlinear integro-differential equation. A key to our mathematical analysis of the FPE is adding a regularization factor into the cost constraint to mitigate the blow-up of the logit function. This property carries over to the McKean-Vlasov SDE. We also present a numerical method based on a naïve finite difference discretization for computing the FPE along with demonstrative computational examples, showing that the regularization method does not critically affect numerical solutions while preventing the breakdown of numerical computation. Finally, we conduct another demonstrative application study in which environmental, energy, and fishery resources intersect.
CommentsVer. June 19, 2026
