兰伯特 W 函数在解决延迟微分方程中用于经济学和金融学建模
Adam Krawiec1, Akio Matsumoto2, Anna Połeć1
1Jagiellonian University, Kraków, Poland.
Nonlinear dynamics, psychology, and life sciences
|December 18, 2025
概括
本研究应用了兰伯特W函数来解决带有延迟的经济模型. 它揭示了延迟如何导致经济增长和市场价格动态的周期性行为和稳定性转变.
科学领域:
- 经济学 经济学 经济学
- 数学建模的数学建模
- 金融数学 金融数学
背景情况:
- 延迟微分方程 (DDE) 对于模拟具有时间滞后的经济和金融系统至关重要.
- 兰伯特W函数是一个特殊的数学函数,在解决复杂方程方面具有应用.
- 了解稳定性和动态制度,特别是周期性行为,对于经济分析至关重要.
研究的目的:
- 为了证明兰伯特W函数在解决经济学和金融相关的DDE中的应用.
- 分析延迟对经济模型的影响,特别关注稳定性和周期动态.
- 为了解经济增长和市场价格波动提供一个数学框架.
主要方法:
- 介绍兰伯特W函数及其分析性质.
- 应用兰伯特W函数来解决延迟微分方程模型.
- 在选定的经济模型中推导周期性行为和稳定性开关的条件.
主要成果:
- 用Solow经济增长模型推导的条件与延迟,显示延迟和人口增长如何相互作用以创建周期性行为和稳定性开关.
- 在延迟供应依赖的市场价格模型中,为波动和稳定性切换的出现建立了准确的条件.
- 证明兰伯特W函数在分析经济DDEs中的稳定性和动态模式方面的有效性.
结论:
- 兰伯特W函数提供了一种有效的技术,用于分析具有延迟的经济模型中的稳定性和动态制度.
- 经济系统的时间延迟可能导致显著的动态行为,包括周期性波动和稳定性的转变.
- 提出的方法论提供了对增长周期的出现和经济和金融环境中持续波动的洞察.
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