Synchronization of Fractional-Order Hyperchaotic Finance Systems Using Sliding Mode Control Techniques

In this chapter, the basic concepts of fractional-order dynamical systems are presented, and the synchronization methodologies of fractional order chaotic dynamical systems are established using slide mode control techniques. Through observation of the different phase portraits and time-series graphs of fractional order finance systems through utilization of the fractional calculus and computer simulation, the authors have obtained that the lowest dimension of fractional order hyper chaotic finance system is 3.90, which is less than 4. Bifurcation diagrams and Lyapunov exponents of fractional order hyper chaotic finance system are calculated to justify the chaos in the systems. Synchronization of two identical fractional-order hyper chaotic finance systems are achieved using sliding mode control techniques.