Abstract
This paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model’s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system’s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement.
Highlights
In the last decade, chaos theory has attracted many researchers
Chaos theory is a field of mathematics that can be applied in many domains: from modeling chaotic financial systems [1], in representing circuit schematics [2, 3], and others. e chaotic systems and their circuit schematics have received many investigations in the literature, see, for example, [2,3,4]
We provide in this paper that the initial conditions impact the chaotic behaviors in the fractional context. e circuit schematic of the fractional chaotic system and the results after simulation in Multisim confirm the theoretical findings obtained via the numerical scheme
Summary
Chaos theory has attracted many researchers. Chaos theory is a field of mathematics that can be applied in many domains: from modeling chaotic financial systems [1], in representing circuit schematics [2, 3], and others. e chaotic systems and their circuit schematics have received many investigations in the literature, see, for example, [2,3,4]. They present a novel numerical scheme for the used fractional operator to depict the phase portraits of their proposed chaotic system. Ey provided a numerical scheme to depict the considered model’s phase portrait in the fractional operators’ context. In [16], Li et al introduce a new four-wing model with integer-order derivative, which will be subject to investigations in the fractional context. We finish with the final remarks and future perspectives of research
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