A novel financial system with one stable and two unstable equilibrium points: Dynamics, coexisting attractors, complexity analysis and synchronization using integral sliding mode control

In the world of economics, financial risk is a significant issue that concerns countries and all economic agents. It refers to the potential for experiencing losses due to unpredictable fluctuations in financial or investment activities caused by endogenous factors. Chaos theory provides an explanation for the complexity observed in economic time series, as it supports an endogenous view. This article proposed an enhanced chaos-based financial risk system with one stable and two unstable equilibrium points. The existence of stable and unstable equilibrium points shows that the proposed system has both hidden and self-excited chaotic attractors. By analyzing its dynamic behavior, the study unveils the transition from stability to chaos in the improved financial risk system, while also describing how the complex dynamics of the system affect changes in financial market risk. In addition, this study explores the fundamental dynamic behavior of the financial risk system, including stability analysis, Lyapunov exponent, bifurcation analysis, coexisting attractors, 0-1 test, algorithm and spectral entropy (SE). Finally, with the help of integral sliding mode control (ISMC), we discover the outcomes for the asymptotic synchronization of two chaotic financial systems that are constructed as master and slave systems. Simulations are provided to accompany and support the findings from this research.