A fractional-order hyper-chaotic economic system with transient chaos

Abstract

We introduce for the first time a fractional-order hyperchaotic economic system. In this system, chaos generation depends upon the value of fractional-order. For certain fractional orders, a sustained regime of chaos is obtained. Also, the transient chaos phenomenon is detected for lower fractional orders. The dynamical behavior of the system is numerically investigated using bifurcations diagrams, basins of attraction, and Lyapunov exponents. Next, an adaptive terminal sliding mode control (ATSMC) with neural network estimator for finite-time stabilization and synchronization of the fractional-order system has been proposed. The radial basis function (RBF) neural network is used to achieve the estimation of the unknown function of the system. Also, the effects of external disturbances are fully taken into account with neural network estimator. The weights of the RBF neural network are updated based on the appropriate adaptation law. Using the fractional version of the Lyapunov stability theorem, the finite-time convergence of the closed-loop system has been proven. Finally, the new control technique is used for control and synchronization of the fractional-order hyperchaotic economic system. Simulation results illustrate the effectiveness of the proposed control scheme for uncertain fractional-order systems in the presence of external disturbances.