Tracking Dynamic Bifurcations and Predicting Tipping Points in Time-Dependent Stochastic Financial Systems

This study proposes an improved stochastic financial dynamical model to investigate the nonlinear dynamics influenced by noise and time-varying parameters. The Reservoir Computing (RC) is employed to predict the system’s tipping point and is compared with neural networks and sparse identification of nonlinear dynamical systems approaches. Experimental results demonstrate that RC outperforms traditional methods in predicting the tipping point, accurately identifying key turning points in the system. Notably, RC is trained solely on data from the stable regime, avoiding the common limitation of requiring post-transition information. By integrating stochastic dynamics with machine learning techniques, this study provides a novel framework for understanding and forecasting the tipping point in financial systems, offering theoretical support for early warning of systemic risk.