Abstract
This chapter announces a new chaotic finance system and show that it is a self-excited chaotic attractor. The phase portraits and qualitative properties of the new chaotic system are described in detail. An electronic circuit realization of the new chaotic finance system is carried out to verify the feasibility of the theoretical model. Next, this chapter examines the control and synchronization of the new chaotic financial system with uncertain parameters as well as known parameters using adaptive control and backstepping control techniques. The designed adaptive controller control and globally synchronizes two identical chaotic financial systems evolving from different initial conditions. The designed controller is capable of stabilizing the financial system at any position as well as controlling it to track any trajectory that is a smooth function of time. Numerical simulations are presented to demonstrate the feasibility of the proposed schemes.
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