Double well stochastic resonance for a class of three-dimensional financial systems

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.