Simulated dynamics complexity of fractional financial system with price index

The price index is closely related to investment cost and interest rates; this study primarily focused on the exploration of the dynamic characteristics within a category of fractional-order financial systems with the price index, interest rates, and investment demand, utilizing chaos and bifurcation theories. Initially, the investigation delved into the existence and singularity of the solution set. Subsequently, the systemic stability and equilibrium points were scrutinized. Crucially, through the application of a predictive-correction numerical method, simulations were conducted to illustrate the price index bifurcation diagrams and phase portraits under varying system parameters. The impact of diverse financial indicators on the system was simulated, revealing the system’s complexity evaluation behavior under different parameter settings. The outcomes of this research significantly contribute to the comprehension of the system dynamics.