Coexisting attractors, crisis route to chaos in a novel 4D fractional-order system and variable-order circuit implementation

• Published in: European physical journal plus Vol. 134; no. 2; p. 73
• Main Authors: Zhou, Chengyi, Li, Zhijun, Xie, Fei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Behavior; Bifurcations; Calculus; Chaos theory; Circuit design; Complex Systems; Condensed Matter Physics; Coordinate transformations; Dynamical systems; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Ordinary differential equations; Parameters; Physics; Physics and Astronomy; Regular Article; Symmetry; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2019-12434-4

. In this paper, a novel 4D fractional-order chaotic system is proposed, and the corresponding dynamics are systematically investigated by considering both fractional-order and traditional system parameters as bifurcation parameters. When varying the traditional system parameters, this system exhibits some conspicuous characteristics. For example, four separate single-wing chaotic attractors coexist, and they will pairwise combine, resulting in a pair of double-wing attractors. More distinctively, by choosing the specific control parameters, transitions from a four-wing attractor to a pair of double-wing attractors to four coexisting single-wing attractors are observed, which means that the novel fractional-order system experiences an unusual and striking double-dip symmetry recovering crisis. However, numerous studies have shown that the fractional differential order has an important effect on the dynamical behavior of a fractional-order system. However, these studies are based only on numerical simulations. Thus, the design of a variable fractional-order circuit to investigate the influence of the order on the dynamical behavior of the fractional-order chaotic circuit is urgently needed. Varying with the order, coexisting period-doubling bifurcation modes appear, which suggests that the orbits have transitions from a coexisting periodic state to a coexisting chaotic state. A variable fractional-order circuit is designed, and the experimental observations are found to be in good agreement with the numerical simulations.