Modeling, simulation, and backstepping control of the new chaotic monetary system with transient chaos

This paper presents a comprehensive study of a new chaotic monetary system characterized by transient chaos. The proposed system is modeled using an autonomous set of absolute nonlinearity equations, which exhibit chaotic behavior under specific parameter conditions. Through dynamic analysis, including bifurcation diagrams and Lyapunov Exponents (LEs) spectra, the system's intricate behavior is explored, revealing successive chaotic, periodic, and stable motions. The phenomenon of multistability is particularly emphasized, showcasing the existence of multiple coexisting attractors under varying initial conditions. Additionally, the study introduces offset boosting and amplitude control as mechanisms to manipulating the system's chaotic signals, further enhancing the versatility of the model. The concept of transient chaos is also investigated, highlighting the system's ability to transition from chaotic to periodic states over time. To achieve control over the chaotic behavior, a nonlinear backstepping design method is proposed. This control strategy is analyzed and numerically simulated, demonstrating its effectiveness in stabilizing the system and guiding it to desired equilibrium points.