Determining the chaotic behavior in a fractional-order finance system with negative parameters

A fractional-order finance system with negative values for system's parameters is introduced. Based on an integer-order finance system with two nonlinearities, we discovered chaos in new regions for system's parameters. By selecting negative values for system's parameters, the eigenvalues of the proposed system can be modified to decrease the fractional order as low as 1.74, while the asymptotic stability theorems of the fractional systems are satisfied. Complex dynamic behaviors of the proposed system are also analyzed by interesting nonlinear analysis tools such as bifurcation diagram versus fractional order, Lyapunov spectrum versus fractional order, Kaplan-Yorke dimension versus fractional order and a dissipative analysis versus fractional order. Finally, an electronic circuit was designed to synthesize the fractional finance system with negative values.