The significant changes in factors such as interest rates, investment demand, and price indices greatly influence the response patterns of the financial system, bringing about increased uncertainty to financial markets. Exploring methods to enhance financial stability and regulatory capabilities, effectively mitigating market disruptions caused by emerging phenomena, constitutes a highly meaningful research topic. The authors, building upon the foundation of the classic chaotic financial system, constructed a three-dimensional double-well random resonance system by incorporating interest rate-related input signals and conducted theoretical analysis on its dynamical characteristics. In this paper, the periodic signal is set as the economic intervention value at the national level, while the noise signal is set as the external market fluctuation value. The impact of three scenarios on the financial system is analyzed: government intervention, the combined effect of government intervention and external market fluctuations, and minimal government intervention. The results indicate that under appropriate intervention conditions, when external market shocks, considered as noise, impact the financial system, the double-well random resonance system can dissipate them into ordered benign signals, enhancing system stability. This maximizes the potential applications of the financial system, prevents financial instability, and provides decision-making references for government regulation of the financial system under certain conditions.

中文翻译：

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一类三维金融系统的双井随机共振


利率、投资需求、物价指数等因素的显着变化极大影响金融体系的反应模式，给金融市场带来不确定性增加。探索增强金融稳定和监管能力的方法，有效缓解新兴现象造成的市场扰乱，是一个非常有意义的研究课题。作者在经典混沌金融系统的基础上，结合利率相关输入信号构建了三维双阱随机共振系统，并对其动力学特性进行了理论分析。本文将周期信号设为国家层面的经济干预值，将噪声信号设为外部市场波动值。分析了三种情景对金融体系的影响：政府干预、政府干预与外部市场波动的综合效应以及政府最小干预。结果表明，在适当的干预条件下，当外部市场冲击被视为噪声冲击金融系统时，双井随机共振系统可以将其消散为有序的良性信号，增强系统的稳定性。这最大限度地发挥了金融体系的潜在应用，防止金融不稳定，并在一定条件下为政府监管金融体系提供决策参考。