Hidden chaotic attractors and self-excited chaotic attractors in a novel circuit system via Grünwald–Letnikov, Caputo-Fabrizio and Atangana-Baleanu fractional operators
A.E. Matouk, Monica Botros
Abstract
Recently, the study of hidden and self-excited attractors has drawn considerable significance in dynamical systems due to its potential applications in nature and industry. Here, a new circuit system is proposed. A circuit realization of the system’s circuit is designed. The existence of hidden chaotic attractors and self-excited chaotic attractors is studied when the Grünwald–Letnikov, Caputo-Fabrizio, and Atangana-Baleanu-Caputo operators are implemented into the proposed system. A comparative study is conducted to discuss the impact of the three different operators on the new system. The comparison between the operators shows that the Grünwald–Letnikov operator is better than the Caputo-Fabrizio and Atangana-Baleanu-Caputo operators in handling the chaotic dynamics of the new system. On the other hand, the time consumed by the Caputo-Fabrizio operator is less than its counterpart by the Atangana-Baleanu-Caputo operator in all simulations.