FOUR-WING ATTRACTORS: FROM PSEUDO TO REAL

Abstract

Some basic dynamical behaviors and the compound structure of a new four-dimensional autonomous chaotic system with cubic nonlinearities are investigated. A four-wing chaotic attractor is observed numerically. This attractor, however, is shown to be an numerical artifact by further theoretical analysis and analog circuit experiment. The observed four-wing attractor actually has two coexisting (upper and lower) attractors, which appear simultaneously and are located arbitrarily closely in the phase space. By introducing a simple linear state-feedback control term, some symmetries of the system and similarities of the linearized characteristics can be destroyed, thereby leading to the appearance of some diagonal and anti-diagonal periodic orbits, through which the upper and lower attractors can indeed be merged together to form a truly single four-wing chaotic attractor. This four-wing attractor is real; it is further confirmed analytically, numerically, as well as electronically in the paper. Moreover, by introducing a sign-switching control function, the system orbit can be manipulated so as to switch between two equilibria or among four equilibria, generating two one-side double-wing attractors, which can also be merged to yield a real four-wing attractor.