Numerical Procedure and its Applications to the Fractional-Order Chaotic System Represented with the Caputo Derivative

This chapter focuses on a numerical procedure and its application to a fractional-order chaotic system. The numerical scheme will discuss the Lyapunov exponents for the considered model and characterize the chaos’s nature. We will also use the numerical scheme to depict the phase portraits of the proposed fractional-order chaotic system and the bifurcation maps. Note that the bifurcation maps are used to characterize the influence of the different parameters of our considered fractional model. The impact of the initial conditions and the coexisting attractors will also be analyzed. With the coexistence, the new types of attractors will be discovered for our considered model. To confirm the investigations in this chapter, the proposed model will be applied to the electrical modeling. Therefore, the circuit schematic of the considered fractional model will be implemented in real-world problems. And we notice good agreement between the theoretical results and the results obtained after Multisim simulations. The stability of the equilibrium points of the presented model will also be focused on details and will permit us to delimit the chaotic region in general.