Investigation of Chaotic Behavior, Rotational Symmetry, Multistability and Dynamic Analysis for a New Chaotic 4-D Finance System

This study explores the chaotic behavior, rotational symmetry, multistability, and dynamic properties of a newly proposed 4-D finance system (N4DFS), modified from the Lu financial model by incorporating an absolute function nonlinearity. This modification increases the system’s complexity, leading to a more chaotic attractor, evidenced by a higher maximal Lyapunov exponent (MLE) compared to the original Lu system. The system exhibits rotational symmetry about the y-axis and shows the saddle points. Bifurcation Analysis (BA) shows that the system transitions between chaotic, periodic, and stable states, depending on parameters (a, b, c, p, q). Multistability is also demonstrated through the coexistence of different attractors under varying initial conditions. Furthermore, Offset Boosting Control (OBC) enables flexible amplitude adjustments while maintaining the system’s overall dynamic behavior. This research contributes to the understanding of chaotic financial models and offers insights for future studies in chaotic systems and financial dynamics.