Self-Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems

Abstract

Self-excited and hidden chaotic attractors are interesting complex dynamical phenomena. Here, Matouk’s hyperchaotic systems are shown to have self-excited and hidden chaotic attractors, respectively. Two case studies of hidden chaotic attractors are provided which are examined with orders 3.08 and 3.992, respectively. Moreover, self-excited chaotic attractors are found in the fractional-order system and its integer-order counterpart. The existence of one-eyed face self-excited chaotic attractors is also reported in this work. Our results show that the fractional derivative affects the appearances of hidden chaotic attractors in this system.