Chinese Dynastic Cycles of Corruption and Power

This study models the cyclical rise and fall of Chinese dynasties through the interplay of power and corruption using the Van der Pol equation. It captures the historical pattern where dynasties emerge with low corruption and rising power, reach a peak, and collapse as corruption undermines authority. The Van der Pol model, known for generating self-sustaining cycles, reflects how early dynastic reforms drive rapid power growth, while increasing corruption accelerates decline and collapse. The system then resets, mirroring the continuous rise and fall observed in Chinese history. Additionally, the study analyzes the evolution of the system's total energy, revealing how power and corruption interact to drive cycles of expansion, instability, and collapse. Simulations further show how cor ruption feedback intensity influences the length and stability of dynastic cycles, explaining why some dynasties, like the Han and Tang, endured longer than others, such as the Song and Ming. This research offers a quantitative framework to understand the repetitive nature of dynastic cycles driven by power and corruption.