Lambert W Function in Solving Delay Differential Equations for Modeling in Economics and Finance
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Summary
This summary is machine-generated.This study applies the Lambert W function to solve economic models with delays. It reveals how delays can cause cyclical behavior and stability shifts in economic growth and market price dynamics.
Area Of Science
- Economics
- Mathematical Modeling
- Financial Mathematics
Background
- Delay differential equations (DDEs) are crucial for modeling economic and financial systems with time lags.
- The Lambert W function is a special mathematical function with applications in solving complex equations.
- Understanding stability and dynamical regimes, particularly cyclical behavior, is vital in economic analysis.
Purpose Of The Study
- To demonstrate the application of the Lambert W function in solving DDEs relevant to economics and finance.
- To analyze the impact of delays on economic models, specifically focusing on stability and cyclical dynamics.
- To provide a mathematical framework for understanding fluctuations in economic growth and market prices.
Main Methods
- Introduction to the Lambert W function and its analytical properties.
- Application of the Lambert W function to solve delay differential equation models.
- Derivation of conditions for cyclical behavior and stability switches in chosen economic models.
Main Results
- Conditions derived for the Solow economic growth model with delay, showing how delay and population growth interact to create cyclical behavior and stability switches.
- Exact conditions established for the emergence of fluctuations and stability switches in a market price model with delayed supply dependence.
- Demonstration of the Lambert W function's effectiveness in analyzing stability and dynamical regimes in economic DDEs.
Conclusions
- The Lambert W function provides an effective technique for analyzing stability and dynamical regimes in economic models with delays.
- Time delays in economic systems can lead to significant dynamic behaviors, including cyclical fluctuations and shifts in stability.
- The methodology presented offers insights into the emergence of growth cycles and constant fluctuations in economic and financial contexts.
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