A novel fractional-order chaotic financial system with external disturbances: dynamic analysis, stabilization, and adaptive synchronization

This study investigates the impact of a chaotic financial systems with external disturbances. Firstly, an improved financial system that exhibits enhanced chaotic behavior was constructed by adding a new quadratic term and adaptive parameters. Through the analysis of the Lyapunov exponents, phase diagrams, and equilibrium points, it is demonstrated that complex chaotic dynamics persist. Secondly, Recognizing the broader applicability of fractional order systems, the system is further extended to fractional dimensions, with corresponding dynamic analysis provided. Thirdly, to address chaotic behaviors, the dynamic feedback control and adaptive projective synchronization are proposed. The dynamic feedback gain controller can quickly stabilize the unstable equilibrium point of the system to the origin. When parameter uncertainties, the synchronization of the system is realized by adaptive projective control. Numerical simulations verified the above contents and proved their effectiveness in regulating chaotic dynamics under different initial conditions and disturbances.