A new 3D fractional-order chaotic system with complex dynamics

Abstract

Compared to integer-order chaotic systems, fractional-order chaotic systems have more complex dynamical features due to the introduction of order. The application of fractional-order chaotic systems to chaotic cryptosystems makes the cryptosystems with higher security properties. In this paper, we developed a new 3D fractional-order chaotic system from a 3D integer-order chaotic system, and investigate the dynamical behaviors of this fractional-order system with different parameters and orders. Moreover, self-excited attractors appeared at lower orders through circuit simulations. Furthermore, the synchronization of the new fractional-order chaotic system in the presence of systematic uncertainties and perturbations was achieved using the sliding mode control technique, which sets the stage for the implementation of communication. Finally, offset boosting control was used to investigate the utility of the new chaotic system in engineering applications.

Electrical characteristics of a fractional-order 3 × n Fan network

“…People have found that actual LC circuits are usually FO [8][9][10][11][12][13][14][15][25][26][27][28][29][30][31][32][33][34][35][36][37]; therefore the study of FOCs has practical application value. In this article, our results make some theoretical contributions to the development of FO 3 × n Fan circuit networks.…”

“…References [30][31][32][33] have had a significant impact on the definition and research of fractional calculus. In recent years, a number of researchers have devoted themselves to the study of FOC theory [34][35][36][37]; among them, some of the literature focuses on physical analysis [34], some focus on circuit models [35], while others focus on mathematical analysis [36,37]. Researchers have found that the study of FOCs can be directly implemented using resistor network theory, and numerous studies have made many achievements in the study of resistor network models.…”