Imperfect chimeras in a ring of four-dimensional simplified Lorenz systems

Analyzing the dynamics of networks of coupled oscillators possessing chimera states has attracted considerable attention in recent years. Here we study a ring of coupled 4D simplified Lorenz systems whose prototype was first studied by Li and Sprott [1]. An interesting feature of this system is the coexistence of a limit cycle and two symmetric strange attractors for some specific range of parameters. Investigating a network of this type under long range interactions, we find a multitude of very interesting chimera multi-chimera states, whose appearance we relate to initial conditions chosen within the basins of attraction of the limit cycle and strange attractor of the individual 4D system. Thus, for sufficiently low coupling, selecting more and more initial conditions from the strange attractor basins leads to one or more “rebel” particles departing from the synchronous group and producing fascinating “imperfect” chimera states. For larger coupling these “rebels” multiply and the system develops what one might call “perfect” chimera states with multiple “heads”.