Dynamic analysis of a new 4D fractional-order financial system and its finite-time fractional integral sliding mode control based on RBF neural network

In this paper, considering the combined effect of interest rate and investment demand on the price index, a new 4D fractional-order financial system is established. Based on the local stability theory, the stability of equilibrium points and static bifurcation phenomena are discussed. Subsequently, to further analyze the dynamic behaviors of the new financial system, numerical tools such as bifurcation diagrams, Lyapunov exponents, phase diagrams, 0–1 test diagrams, and complexity diagrams are employed. It is found that, for a suitable selection of the differential order or system parameter, the proposed system can generate periodic oscillations with different period and chaotic attractors with different shapes. Furthermore, a new controller combining radial basis function (RBF) neural network with fractional-order integral sliding mode control is proposed to realize the finite-time synchronization for a class of fractional-order systems. Finally, the effectiveness of the presented control scheme is verified by numerical simulations and the influence of RBF neural network parameters on the control performance is analyzed.