Abstract
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.