Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rossler-Like System

A new Rossler-like system is constructed by the linear feedback control scheme in this paper. As well, it exhibits complex dynamical behaviors, such as bifurcation, chaos, and strange attractor. By virtue of the normal form theory, its Hopf bifurcation and stability are investigated in detail. Consequently, the stable periodic orbits are bifurcated. Furthermore, the anticontrol of Hopf circles is achieved between the new Rossler-like system and the original Rossler one via a modified projective synchronization scheme. As a result, a stable Hopf circle is created in the controlled Rossler system. The corresponding numerical simulations are presented, which agree with the theoretical analysis.